Open Tahzib Safwat - Dissertation

The Pennsylvania State University The Graduate School College of Engineering

MODELING AND DESIGN OF WEARABLE TRANSDUCERS FOR

ASSISTIVE TECHNOLOGIES

A Dissertation in Mechanical Engineering by Tahzib Safwat

Submitted in Partial Fulﬁllment of the Requirements for the Degree of

Doctor of Philosophy

August 2019 The dissertation of Tahzib Safwat was reviewed and approved∗ by the following:

Christopher D. Rahn Associate Dean for Innovation and Professor of Mechanical Engineering Dissertation Co-Advisor, Co-Chair of Committee

Zoubeida Ounaies Professor of Mechanical Engineering Dissertation Co-Advisor, Co-Chair of Committee

Mary I. Frecker Professor of Mechanical Engineering

Mehdi Kiani Assistant Professor of Electrical Engineering

Karen A. Thole Distinguished Professor of Mechanical Engineering Department Head of Mechanical Engineering

∗Signatures are on ﬁle in the Graduate School.

ii Abstract

Wearable technology is a growing and highly interdisciplinary field, with research being conducted in many areas, including micro-electromechanical systems (MEMS), flexible sensors and actuators, energy harvesting, and human factors. In this dissertation, facets of wearable technology that are beneficial to healthcare and assistive technologies are explored. Polyvinylidene fluoride (PVDF) terpolymer actuators are applied to wearable haptics, electromagnetic (EM) harvesters are compared to PVDF films as strain energy harvesters, PVDF copolymer films are used for body-based energy harvesting, and a statistical analysis of an energy harvesting system model with storage is presented. People with prosthetic limbs can benefit from having haptic feedback that mimics a sense of touch. Electroactive polymer (EAP) actuators made of PVDF terpolymer, P(VDF-TrFE-CFE), have the potential to fill this need due to their compliance and ability to provide high strains. An EAP unimorph actuator is modeled for haptic feedback applications and shown to have flexibility, high frequency vibration capability (3mm end-to-end tip deflection at a resonance of 429Hz for a 10mm long beam), and high amplitude vibration at low frequency (tip deflection of up to 825µm for 10mm long beam) that provides a new way to send haptic signals by combining high frequency vibration with a slowly varying DC offset. A linear time- varying model is validated with experiments under static and slowly varying bias voltages. These actuators are demonstrated in a prosthetic feedback application and rotary motor prototype. The rotary motor is also used to calculate the maximum power density of the EAP active material, of at least 0.27W/g in the unimorph configuration, competitive with electric motors. Continuous monitoring of patients using low power sensors can help in tracking and treatment of chronic illnesses and other health conditions. Chest motion is investigated as a continuous source of strain energy from the body to power wearable health monitors. EM generator and piezoelectric PVDF film harvesters are modeled, designed, and experimentally tested. Static friction effects in the EM generators and their bulky profile make them poorly suited to this application. Piezoelectric PVDF films produce much lower power than EM, but their power scales with surface area and the films can be integrated into textiles. Under the

iii force required by the EM harvester to break away from static friction, a PVDF film of 100cm2 can produce up to 10µW. This, combined with their low weight and bending stiffness, make them ideal for wearables. To increase the power output from wearable piezoelectric energy harvesters, the PVDF copolymer, P(VDF-TrFE), connected in 33-mode via interdigitated electrodes (IDEs), is investigated. Copolymer is a highly compliant multifunctional material with superior electromechanical properties. Model-based analysis shows that its output power per force, a metric important for comfort, is greater than PVDF. A novel electrode design, interlaminar grid electrodes (IGEs), is used to align strain and poling directions similar to IDEs. However, electrodes of opposite electrical polarity are applied on different surfaces of the copolymer films, as in parallel plate electrode (PPE) configurations, helping to reduce fabrication defect-related shorting and open circuits. The ability to pattern electrodes with micron-scale features such as IGEs over large areas of copolymer thin films is a great asset to building wearable electromechanical devices. Additionally, the ability to pattern micron-sized electrode features at the interface between the layers of multilayer copolymer is required for IGEs and improves the performance of IDEs. A process to create multilayered copolymer with patterned electrodes using PVA and alumina capping layers is presented. Although alumina has closer dielectric properties to copolymer, very thin layers of PVA provide good chemical resistance without affecting the capacitance of the device. The self-power ability of a wearable device depends on how much energy is available for harvesting. Energy availability strongly depends on human behavior, including the activities that people do and the environments that they do them in. The intermittency of power generation limits the ability of an energy harvester to self-power a wearable device. Information from databases on human behavior and solar irradiance are used to estimate the average power that can be harvested from large populations. For three demographic groups (retired people, children, and office professionals), mechanical, thermoelectric, and photovoltaic harvesters worn on the wrist/forearm are simulated with supercapacitors that bridge power mismatches between the harvested power and power demand (assumed constant). The average solar power harvested, approximately 50-70µW, is an order of magnitude higher than mechanical or thermoelectric power, both of which harvest less than 10µW on average. Intermittency causes the solar (and mechanical) energy harvesters to achieve a 90% success rate of self-powering when the constant power consumption is a low 30-35% of their average harvested power. Thermoelectric generators, on the other hand, can provide 87% of their average harvested power with 90% success rate.

iv Table of Contents

List of Figures viii

List of Tables xiii

Acknowledgments xiv

Chapter 1 Introduction 1 1.1 Research Motivation ...... 1 1.2 Haptic Feedback Using Electroactive Polymer Actuators ...... 2 1.3 Harvesting Energy from Chest Motion ...... 4 1.4 Electromagnetic and Piezoelectric Energy Harvesters ...... 5 1.5 Flexible Thin Film Piezoelectric Energy Harvesters ...... 6 1.6 Energy Harvesting and Storage Systems for Body Sensor Networks . 8 1.7 Dissertation Outline ...... 10 1.8 Key Contributions ...... 12

Chapter 2 Evaluation, Modeling, and Applications of Electrostrictive Uni- morph Actuators 13 2.1 Introduction ...... 13 2.2 Background and Initial Observations ...... 13 2.2.1 Viscoelasticity and Hysteresis ...... 15 2.2.2 Power Dynamics ...... 17 2.2.3 Current Haptic Technology ...... 18 2.3 Actuation Model ...... 18 2.3.1 Model Derivation ...... 19 2.3.2 Point Force and Mean Power ...... 26 2.3.3 Time-Varying Simulation Method ...... 27 2.4 Results and Discussion ...... 28

v 2.5 Rotary Motor ...... 31 2.5.1 Design ...... 32 2.5.2 Performance ...... 33 2.5.3 Discussion ...... 35 2.6 Haptic Band for Prosthetic Feedback ...... 35

Chapter 3 Modeling and Design of Electromagnetic and Piezoelectric Chest Strain Energy Harvesters Including Soft Tissue Eﬀects 37 3.1 Introduction ...... 37 3.2 Harvester Types ...... 37 3.3 Derivation of the Electromagnetic Generator Model ...... 38 3.3.1 Electromagnetic Harvester Model with Soft Tissue Compliance 40 3.4 Derivation of the PVDF Harvester Model ...... 42 3.4.1 PVDF Harvester Model with Soft Tissue Compliance . . . . 45 3.5 Experiment and Validation ...... 45 3.5.1 Electromagnetic Generator Model Validation ...... 45 3.5.2 PVDF Model Validation ...... 47 3.6 Power Output ...... 49 3.7 Simulation of Soft Tissue Eﬀects ...... 50

Chapter 4 Model-Based Analysis of P(VDF-TrFE) Energy Harvesters with Interdigitated Electrodes 53 4.1 Introduction ...... 53 4.2 P(VDF-TrFE) Energy Harvesters in d33 Mode ...... 53 4.2.1 Modeling of Interdigitated Electrodes ...... 56 4.2.2 Model Based Comparison of PVDF and P(VDF-TrFE) . . . 58 4.2.3 Multilayer Interlaminar Grid Electrodes ...... 58 4.3 Simulation and Analysis ...... 61 4.3.1 Electric Field Exposure to Human Body ...... 64

Chapter 5 Multilayered Fabrication Procedure for Micron-Scale Electrodes on P(VDF-TrFE) 66 5.1 Introduction ...... 66 5.2 Fabrication ...... 66 5.2.1 Creating Multiple Layers ...... 68 5.2.2 Defect Reduction Using Multilayer Fabrication ...... 68 5.3 Physical Characteristics of Fabricated Copolymer Samples . . . . . 70

vi 5.4 Electrical Characteristics of Fabricated Copolymer Samples . . . . . 74

Chapter 6 Self-Power Analysis of Wearable Devices Using Human Behav- ioral Data 75 6.1 Introduction ...... 75 6.2 Estimating Harvested Power from Human Behavior ...... 76 6.2.1 Mechanical Power ...... 77 6.2.2 Thermal Power ...... 80 6.2.3 Solar Power ...... 82 6.2.4 Demographic Data ...... 84 6.3 Energy Storage Model ...... 87 6.3.1 Model Derivation ...... 87 6.3.2 Computation Process ...... 90 6.4 Monte Carlo Simulation ...... 93 6.4.1 Performance and Discussion ...... 93

Chapter 7 Conclusions and Future Work 96 7.1 Conclusions ...... 96 7.2 Future Work ...... 98

Appendix A Electroactive Polymer Rotary Motor Model 101 A.1 Parameters ...... 101 A.2 Equilibrium Condition ...... 102 A.3 Switched Linear Time-Varying System ...... 103 A.4 State Space Representation ...... 103

Appendix B Detailed Fabrication Steps for Multilayer P(VDF-TrFE) with Micron-Scale Electrodes 107 B.1 Fabrication Process Outline ...... 107

Appendix C Full List of CHAD Activities and Locations 112

Bibliography 115

vii List of Figures

2.1 (Top) Photo of Novasentis actuators epoxied to a base. The copper colored layer is active and the semi-transparent layer is passive. (Bottom) Magnified view of the thickness of the actuator...... 14 2.2 Experimental response of EAP cantilever tip: (a) displacement to a 100V step input and (b) a magnified plot of the same response; (c) scaled charge and displacement frequency responses; (d) the hysteresis of the displacement under a triangle voltage wave with a 120s. period, compared to a parabola...... 15 2.3 Polarization loop of a ferroelectric material before (A) and after (B) being converted to a relaxor ferroelectric via irradiation. Figure courtesy of Zhang et al. (1998)...... 16 2.4 Experimental displacement, current, voltage and power step responses normalized by their maximum values shown in the legend. . 17 2.5 Eccentric rotating mass (top) and linear resonant (bottom) actuators. Image courtesy of Texas Instruments...... 19 2.6 Free body diagram of the actuator in (top) cantilever and (bottom) pinned configurations...... 21 2.7 Simulation of 100V step input compared to experiment. For step responses, V (t) = Vavg(t), hence VL(t) = Vavg(t)...... 28 2.8 Simulation of frequency response function compared to experiment at different constant Vavg and the oscillation amplitude is 50V, i.e. V (t) = 50 sin 2πft + Vavg...... 29 2.9 Dynamic response (top) starting from zero initial conditions with V (t) = 50 sin 4πt+Vavg(t) and Vavg(t) = 25 sin πt+75, and (bottom) starting from steady-state initial conditions at 75V with V (t) = 50 sin 2πt + Vavg(t) and Vavg(t) = 25 sin 0.5πt + 75...... 30 2.10 Estimation of output power by applying tip damping to the actuator model and varying ctip to match impedance...... 31

viii 2.11 Rotary motor with five EAP actuators. The rotor (black) can be seen inside the outer housing (gray) resting on the actuators (brown). The largest cylindrical part of the motor has a diameter of 10.5cm and a height of 4.2cm...... 32 2.12 Motor torque and power vs. speed (top) using five actuators for different frequencies and (bottom) at 9Hz for different numbers of actuators. The length of the red line shows the power contribution of one actuator near the maximum power of the motor...... 34 2.13 A haptic feedback system for a prosthetic foot using force sensitive resistors (FSRs) to calculate balance information and using a haptic band made of EAP actuators to convey that information to the user. 36

3.1 Prototypes of EM harvester (left) and PVDF harvester (right). . . . 38 3.2 Schematic of the rotary EM generator unit (a) and the energy harvester with soft tissue compliance (b). Photos of a prototype EM chest strain energy harvester including the harness (c) and internal components of the harvester assembly (d)...... 40 3.3 Schematic of the PVDF harvester (left) and 3D model of the prototype (right)...... 43 3.4 Output voltage simulation (red) versus experiment (black) for the EM generator in response to sinusoidal input rotations (θl(t)) at 0.3, 0.6, and 0.9 Hz...... 44 3.5 EM generator average power (top plot) measured (circles) and simulated (lines) versus the load resistance under sinusoidal input rotation with frequencies of 0.3, 0.6, and 0.9Hz shown using dark, medium, and light colored lines, respectively. PVDF peak power (bottom plot) measured (circles) and simulated (lines) versus the load resistance under 0.17% strain amplitude sinusoidal input with frequencies of 0.5, 0.75, and 1 Hz shown using dark, medium, and light colored lines, respectively...... 47 3.6 EM harvester prototype simulated mean power versus return spring constant, km, and soft tissue modulus, Es. Plots A and B on right show the corresponding EM harvester time responses...... 51 3.7 PVDF harvester prototype simulated mean power versus passive material stiﬀness, ki, and soft tissue modulus, Es, for a 70 cm × 3 cm PVDF strip...... 52

ix 4.1 (a) Photo of a typical IDE pattern where the harvesting area is the portion of the device that generates voltage when stretched and the rails that connect all of the branches are on the left and right of the harvesting area, (b) schematic of IDE across three electrodes showing the material (white), electrodes (red), and electric field lines (green), and (c) a simplified schematic for modeling. The dead zone under the electrode generates a negligible amount of electricity when the material is stretched axially. The circle in the coordinates represent an arrow pointing out from the page...... 54 4.2 PVDF (solid) and copolymer (dashed) power output per input force at different load resistances under 2N input forcing amplitude. Comparison of (a) PVDF with PPEs and copolymer with IDEs and (b) both PVDF and copolymer with IDEs. The dark, medium, and light lines represent 0.5, 0.75, and 1Hz, respectively...... 59 4.3 Illustration of IGE layers. The device would be strained in the direction of the curved electrodes. Each layer contains an electrode of a different polarity. The same pattern is used in all layers, opposite polarities are just shifted by half a grid size...... 60 4.4 (a) Finite element models and representative volume elements of IDE and IGE. Ratio of simulated electric field (EFEA) to modeled electric field (ETH ) in the (b) active zone and (c) dead zones for different aspect ratios (se/tp). The net vertical electric field for the IDE is zero in the simulation...... 62 4.5 The electric field from an IGE device (shown by the black rectangle at the center) inside PDMS matrix (r = 2.8). The colors represent electric field magnitude (V/m)...... 64

5.1 Fabrication process of copolymer with IGE: (1) Create first copolymer layer and spin coat a layer of photoresist, (2) pattern resist, (3) evaporate electrode, (4) lift-off electrode, (5) create capping layer of PVA (spin coating) or alumina (evaporation), and (6) create second layer of copolymer...... 67 5.2 IDE and IGE patterned on a layer of copolymer. Shorts on the IDE caused by surface defects and electrode delamination are shown by black arrows. The IGE has three broken branches due to a surface defect, as shown by the red circle, but that does not stop the flow of current due to the grid design. A defect that does not cause a short in an IDE can generate a high electric field when poling, shown in the red square...... 69

x 5.3 Microscopic view of the electrodes of the PVA-capped (top) and alumina-capped (middle) two-layer copolymer IGE samples and a sample with IDEs set on a single layer of copolymer (bottom). . . . 71 5.4 Microscope image of the chromium/gold electroded sample (top) and the aluminum eletroded sample (bottom). The aluminum electrode was patterned on top of the alumina capping layer, so cracking on the capping layer broke the electrodes apart as well...... 72 5.5 Capacitance and loss tangent (tan δ) are shown for each sample. The electrode widths are 6µm and the electrode spacing is 24µm. The schematic shows that the electric field (green) can avoid the capping layer in the IDE configuration but must go through it in the IGE configuration...... 73

6.1 System model block diagram. The activity levels and environmental conditions are estimated from the human activity database and NREL solar irradiance data. The power produced by the energy harvesters is calculated, and losses due to power conversion electronics are applied. Power flows to the wearable device for usage or a supercapacitor (with coulombic efficiency and current leakage) for storage...... 76 6.2 The average power harvested by the three types of energy harvesters used in this simulation for different demographics based on CHAD data. The error bars show the standard error. The bottom plots show the maximum power produced each day averaged over the whole set for each harvester. KIN is the mechanical harvester, SOL is the solar harvester, and TEG is the thermoelectric harvester. . . 85 6.3 Average power statistics for kinetic, solar, and thermal harvesters: (a-c) statistical distribution of the time (hour) of maximum power generation, (d-f) average power harvested, and (g-i) power standard deviations. The professional, retired, and children demographic sets are indicated by the dark, medium, and light lines, respectively. . . 88 6.4 Schematic of the supercapacitor model...... 90

xi 6.5 Typical simulation results from a CHAD day (24 hours starting at midnight). a) The solar irradiance, activity level, and outdoor temperature are inputs to the system shown in a normalized plot. b) The temperature difference is based on the location of the individual and the temperature difference across the TEG is calculated using the TEG model. c) The power produced by each harvester, normalized by the average power produced by that demographic using that harvester. d) The cumulative charge entering and exiting the supercapacitor normalized by capacitance and the contributions from each harvester. e) The supercapacitor voltage over time, where the dashed lines represent the upper and lower bounds...... 92 6.6 The success rate of solar (dark), kinetic (medium), and thermal (light) energy harvesters versus power factor. Success is defined as being able to maintain a supercapacitor voltage above 0.5V for 7 (dotted), 21 (dashed), and 63 (solid) days...... 94

A.1 Free body diagram of rotary motor (top) and EAP actuator (bottom). 102 A.2 Simulation output showing rotor tip (blue) and beam tip (red) deﬂection, input voltage, and distance between rotor and beam for 3 diﬀerent spring constants...... 106

C.1 List of CHAD activities with activity level and standard deviation, part 1...... 112 C.2 List of CHAD activities with activity level and standard deviation, part 2...... 113 C.3 List of CHAD locations with probability of time spent in outdoor air and sunlight, part 1...... 113 C.4 List of CHAD locations with probability of time spent in outdoor air and sunlight, part 2...... 114

xii List of Tables

1.1 Harvested power for the diﬀerent energy harvesters...... 10

2.1 Parameter values for EAP actuator...... 27

3.1 Model parameters...... 48 3.2 Breathing energy harvester prototype power levels...... 49

4.1 Material properties of PVDF and P(VDF-TrFE) from TE Connec- tivity and Piezotech Arkema, respectively...... 55

6.1 Relevant CHAD/NREL variables and harvested power for the different energy harvesters...... 78 6.2 Top 10 activity variables in the CHAD database...... 79 6.3 Top 10 location variables in the CHAD database...... 80

xiii Acknowledgments

First and foremost, I would like to thank Dr. Christopher Rahn for being an outstanding advisor and mentor. His patience, guidance, and constant motivation has helped me reach the end of my PhD journey and grow as a researcher. Dr. Rahn has always given me constructive and insightful advice on research, but also encouraged me to explore my own ideas. I am extremely grateful to have Dr. Zoubeida Ounaies as a co-advisor. Her encouragement and approach to problem solving has inspired me to think outside the box for many research problems. I thank them both for being wonderful role models. I would also like to extend my gratitude to my committee members, Dr. Mary Frecker and Dr. Mehdi Kiani, for their patience and advice. I am thankful to have worked with Dr. Michael Grissom and Ryan Tosto from KCF Technologies on my first project at Penn State who were very knowledgeable and patient. Dr. Susan Trolier-Mckinstry, Dr. Shad Roundy, Dr. Mehmet Ozturk, and Dr. Ramakrishnan Rajagopalan provided me with essential guidance in the areas of energy harvesting and energy storage. My thanks also goes to Michael Vecchio, Dr. Saad Ahmed, and Dr. Amira Meddeb, for helping me with experiments and fabrication. I am grateful for the assistance and instruction provided by the technical staff at the Penn State Materials Research Institute as well, especially Dr. Kathleen Gehoski and Dr. Michael LaBella. My former and current labmates and colleagues are the best that I could have asked for: Dr. Tanvir Tanim, Dr. Kentaro Miura, Dr. Mayank Garg, Dr. Xiaokun Ma, Dr. Shawn Treacy, Dr. Matt Krott, Dr. Jun Ma, Nicholas Papavizas, Greg Brulo, George Rai, Mihir Parekh, Matt Lenko, Mike Trowbridge, Dixiong Wang, Dr. Md. Abdullah Masud, Dr. Tanmay Mathur, Ashik Masuk, and Ashwanth Reddy. I am grateful to have loving, encouraging, and supportive parents, Taslima Begum and Sarwar Hussain, and sister, Tasnia Sarwat, who are always there for me at a moment’s notice. I am also grateful to have Sandra Cai Chen in my life, for all of her affection and companionship. I have been extremely fortunate in making many great friends in State College and I am thankful for them all.

xiv This research would not have been possible without ﬁnancial support from the U.S. Army Telemedicine and Advanced Technology Research Center (TATRC) and the National Science Foundation Nanosystems Engineering Research Center (NERC) for Advanced Self-Powered Systems of Integrated Sensors and Technologies (ASSIST). The views and conclusions in this document are those of the authors and should not be interpreted as representing the oﬃcial policies, either expressed or implied, of the the U.S. Government and its institutions.

xv Chapter 1 | Introduction

1.1 Research Motivation

Wearable devices are a class of assistive technologies that have been gaining popu- larity over the last decade due to the advancement of low-powered sensor technology. They can be further enhanced by body-based energy harvesting devices that eliminate the need for batteries. Soft actuators such as electroactive polymers enable haptic signals (i.e. devices that generate forces and vibrations on human skin) to convey information to the wearer—an essential feature for people with disabilities. Wearables facilitate changing the current trend in healthcare from a reactive stance to a proactive one [1]. As a result, wearable health monitoring networks have been a very active field of research and innovation [2–7]. Many products are now offered on the market that allow users to quantify and monitor their level of fitness and monitor their health (e.g. Apple Watch®, FitBit®, etc.). The data generated can help to make preventative care decisions not only for the individuals, but entire populations as well. People with disabilities or chronic diseases could strongly benefit from these technologies, leading to a better quality of life. This thesis takes a comprehensive approach to wearable assistive devices, focusing on the key limitations of actuation for haptic feedback and energy harvesting for self-powered operation. Fundamental contributions are made in the following areas: electroactive polymer (EAP) actuators and devices for haptic feedback, electromagnetic (EM) generators and polyvinylidene fluoride (PVDF) films for chest strain energy harvesting, PVDF copolymer films with patterned electrodes for robust strain energy harvesting, and analysis tools for self-powered wearable devices.

1 Models are developed and validated for the EAP actuators, PVDF harvesters, and EM generators. New fabrication techniques of PVDF copolymer harvesters are presented. A framework for the analysis of wearable energy harvesting and storage systems is developed and simulated on various demographics.

1.2 Haptic Feedback Using Electroactive Polymer Ac- tuators

Smart materials have been studied for centuries as a means of actuation and sensing [8]. In terms of real-world applications, piezoelectric transducers are at the forefront with their utilization in many consumer products such as pressure sensors, accelerometers, gyroscopes, energy harvesters, pumps, ultrasonic devices, etc. [9], and their first implementation over a hundred years ago in sonar devices [10]. Electroactive polymer (EAP) actuators were later discovered as electromechanical devices that can fill some of the needs that piezoelectric materials cannot. The low strain and high stiffness limit the application of ceramic piezoelectric materials in many areas, including “soft” applications, i.e. those that require high compliance and flexibility. Moreover, these applications often involve direct interaction with humans, so lead zirconate titanate (PZT), the most widely used piezoceramic, contains lead making it unsuitable due to health concerns [11, 12], and its potential alternative, potassium sodium niobate (KNN), has been shown to cause environmental damage during its processing [13]. EAPs can be divided into two classes: ionic and electronic [14]. Ionic EAPs actuate through the movement of ions between the electrodes. They can be activated by low voltages, however the actuation is slow (i.e. greater than a fraction of a second) and inefficient. Electronic EAPs, also called field-activated EAPs, polarize spontaneously under an electric field and are able to provide relatively fast actuation rates, but require high electric fields. Electronic polymers can also be either piezoelectric or electrostrictive, meaning their dynamics are approximated by first order equations (i.e. linear voltage-strain function) or second-order equations (i.e. quadratic voltage-strain function), respectively [15]. Typically, both effects exist in electronic EAPs, but one usually dominates. Applications of EAP actuators include microfluidic pumps, focusing lenses,

2 and haptic feedback devices. Usage of EAPs in lenses was proposed as a means of controlling the focal length in optical devices [16]. The timescales for this application are usually large enough to require only static analysis. Microfluidic pumps have also been developed without dynamic modeling of the electroactive material [17, 18]. This is made possible by the steady state oscillatory mode of operation in this application. The haptic devices studied in this thesis would benefit from having a time-domain model. The skin is the largest organ on the human body making the sense of touch an excellent method to interface humans with machines. Haptic feedback systems have seen a great deal of innovation in areas such as virtual reality/remote presence, information security and wearable devices. The inclusion of touch feedback in virtual reality applications adds another dimension of realism and allows important sensory information to be conveyed [19,20], for example, to artfully manipulate objects with remote robotic control or for use in telemedicine. Methods have also been developed to use information from smart sensors in keypads to sense keystroke dynamics in order to detect unauthorized access at secure terminals via pattern recognition techniques [21]. Furthermore, applications exist where vibrating actuators were used inside unlabeled keypads for secure password input in public places [22]. Integration of haptic actuators into clothing or accessories, such as smart watches, would allow for many of the advantages previously mentioned. Additionally, applications have also been developed for use in public health monitoring and rehabilitation [23] and assistive wearable devices, such as guidance systems for the visually impaired [24]. Piezoelectric polymers such as PVDF or P(VDF-TrFE) are soft but exhibit hysteresis, which can be greatly reduced if defects are introduced into the polymer by irradiation [25] or by adding another component [26,27]. The latter process creates the highly compliant relaxor ferroelectric PVDF terpolymer, P(VDF-TrFE-CFE), which exhibits very high strain. These polymers show a good compromise between force and strain, and respond quickly under reasonable voltages. The polymers produce strain through the alignment of molecular dipoles under an electric field. This is the same mechanism undergone by piezoelectric materials when they are poled, however relaxor ferroelectrics do not need poling. The molecular dipoles return to their randomly oriented state once the electric field is removed [28,29]. The material is essentially experiencing the poling process every time it is actuated resulting in very large strains.

3 In practice, the EAP layers must be thin enough to be excited by reasonable voltages yet provide an adequate amount of strain, so unimorphs (i.e. composite bending beams with an electromechanical active layer on a passive substrate) are the logical design because the deflection due to bending is higher than the axial deflection of similar sized actuators. Moreover, transverse vibrations in beams have a much lower natural frequency than axial vibrations, which is important for two reasons: it is exploitable for energy efficiency and it is more likely to be within human tactile perception.

1.3 Harvesting Energy from Chest Motion

The motion of the chest during breathing is the only source of kinetic energy that can be exploited noninvasively when the human body is at rest, making it an ideal energy harvesting source that can continuously generate power for low power applications such as biomedical sensors. Technology developed for chest expansion can also be adapted to generate energy from joint rotation and muscle expansion as well. Energy can be extracted from the respiratory system in two ways: expansion of the chest or airflow of the breath. The latter comes in both implantable [30] and non-invasive devices, but implantable harvesters are a special case that will not be explored here. Non-invasive breath airflow energy harvesters produce low amounts of power and require encumbering equipment [31]. Chest motion is estimated to produce 0.83W of human power [32]. Devices that harvest energy from chest expansion employ several types of energy conversion technologies. PDMS has been used to generate power using the triboelectric effect [33] (i.e. generation of electricity from static charge), producing relatively low maximum power (0.758µW/cm2). The mechanical power of chest strain can be harnessed using piezoelectric materials or electromagnetic (EM) devices. While piezoelectric polymers are well suited to harvest strain energy from the body due to their low bending stiffness and weight, these polymers have relatively low electromechanical coupling and high impedance. EM devices are estimated to have higher energy densities than piezoelectric materials [34], but are bulky, stiff, and have significant friction at the required high gear ratios. Researchers have built an electromagnetic harvester using two DC motor generators and a planetary gear train resulting in an output power of 2mW [35]. An EM

4 harvester with a higher gear ratio yielded a peak power of 15mW [36], but the high gear ratio created high input torque causing user discomfort. Piezoelectric devices offer the advantage of higher sensitivity compared to electromagnetic devices, but also have low electromechanical coupling. For example, a flexible piezoelectric microfiber composite device was sensitive enough to detect heartbeats while harvesting respiration energy, but produced only 15.6µW of peak power compared to an EM device that produced 0.56mW [37].

1.4 Electromagnetic and Piezoelectric Energy Har- vesters

Electromagnetic harvesters primarily operate using either inertia/vibration or directly transform biomechanical force into electricity to provide more power [38]. Inertial harvesters absorb accelerations from the body and oscillate close to resonance to generate power. Researchers explored the power generation capabilities of a generic inertial energy harvester and numerically determined the best harvester properties and the best place to locate the device on the body [39]. However, in practice inertial devices do not offer much flexibility on where to put the device on the body, which limits their maximum size and, consequently, their maximum power. For instance, an inertial device that harvests elbow motion must be worn on the elbow which limits its size to remain ergonomic. Since the power output scales with proof mass value, limiting size also limits power. For example, researchers have developed a backpack that can generate up to 7.4W of power while the user is walking with loads of a few dozen kilograms [40], but the power output drops significantly when the backpack is empty. Smaller devices, such as a wearable EM energy harvester that uses magnetic springs and can generate up to 2.5mW from slow running [41], require activity levels that cannot be maintained to achieve milliwatt scale average power over a 24-hour period. Due to the low velocity of chest motion, direct force kinetic energy harvesters (or strain energy harvesters) are a better way to harvest energy from breathing than vibrational devices. With a direct force device, the generator can be located somewhere convenient, such as the waist, and an ergonomic wearable mechanism can be used to transmit forces from other parts of the body to it. Hence, there

5 is more flexibility in direct-force device sizing as it relates to comfort compared to inertial devices. An example of a direct force device is given by Donelan et al. where a rotary generator was used to harvest energy from the braking action of the knee during walking [42]. An average of 5W was harvested using this device on both legs. For electromagnetic devices, it makes sense to use rotary generators for direct force devices because they allow for more displacement than linear devices per device volume. Additionally, rotational generators can be easily constructed from off-the-shelf components. Piezoelectric polymers have low electromechanical coupling but their lower stiffness and weight provides excellent textile integration characteristics and allows them to be used over larger areas comfortably, proportionally increasing the power output. Researchers have previously integrated piezoresistive materials into clothing for biomedical sensing (i.e. ECG, respiration, motion) [43]. Piezoelectric polymers can be integrated in a similar way to perform the same task while also harvesting energy for self-powered operation. The two most common ways to absorb mechanical strain energy using compliant mechanisms involve direct axial tension and bending. Unimorph devices can make very stiff piezoelectric materials more compliant. However, it is much easier to control the compliance and comfort of a piezoelectric polymer energy harvester by simply attaching a soft material in series and use axial tension.

1.5 Flexible Thin Film Piezoelectric Energy Harvesters

Several piezoelectric harvesters have been developed that use wavy substrates in order to increase compliance in stiff piezoelectric materials through bending, yet use the harvester under axial tension to harvest energy from the low frequency movements of the body. Recently, researchers have reported electrospun 3D printed PVDF fibers on a wavy, flexible substrate [44]. A PVDF sheet with patterned parallel electrodes was also encased in a soft, wavy silicone substrate in order to increase the maximum strain [45]. The patterned electrodes were designed to sum the voltages produced by the segments in tension and compression instead of canceling them out, but this device still used a less efficient piezoelectric mechanism where the poling and strain direction are perpendicular (i.e. 31-mode). The stiffness of PZT, which is the most commonly used piezoelectric ceramic, makes it unsuitable

6 for wearable harvesting, so researchers produced buckled PZT strips by adhering PZT to a pre-stretched substrate [46]. However, even with the enhancement in strain, this device would require a significant support structure due to the brittle nature of PZT and cannot be easily integrated into textiles because of the toxicity of lead [12,12,13]. PZT needs to be made very thin in order to have a low bending stiffness and high compliance as PVDF. It has been shown that PZT experiences a drop in dielectric constant and remnant polarization, and an increase in coercive field as dimensions enter sub-micron scales [47,48]. Wavy harvesters also transform 2D films into 3D structures that protrude from a person’s body [49], which may not be desirable. Wavy structures allow stiffer piezoelectric materials to be used in bending mode through axial tension input. It has been shown that uniform strain in a piezoelectric material yields the highest electromechanical efficiency [50], but uniform strain does not occur in bending mode. Also, the passive layers used in bending devices absorb a portion of the input energy and contribute to inefficiency when used at very low, non-resonant frequencies. Hence, the highest power efficiency can be achieved through pure axial strain. For this reason, many researchers have investigated combining piezoelectricity with other energy conversion methods to create multimodal energy harvesters [51,52]. For piezoelectric polymers, the best way to control stretchability is to put another compliant material in series to control stiffness. In other words, if the polymer film is too stiff for a certain wearable application, a softer textile material can simply be attached in series with the polymer film to reduce the overall stiffness of the wearable device. Additionally, if the polymer film is exceeding its material strain limits, a stiffer textile material (i.e. webbing) that is slightly longer than the polymer film can be attached in parallel to prevent the film from stretching beyond its limits. This provides great design flexibility in a simple way. The copolymer of PVDF, P(VDF-TrFE), is more compliant than PVDF while maintaining similar energy harvesting properties in the poling direction. Additionally, it has been shown that scalable fabrication processes such as dip-coating can be used to create multilayered P(VDF-TrFE) devices [53]. Interdigitated electrode (IDE) patterns allow piezoelectric films to be poled in-plane, thereby aligning the polarization and strain directions and eanbling the use

of the most efficient piezoelectric coefficient, d33. IDEs also allow great flexibilty in controlling the electrical properties of the material, such as output voltage, without

7 having to alter the dimensions of the polymer film. Hence, they are commonly used in surface acoustic wave (SAW) filters. Researchers created an interdigitated electrode design that incorporated serpentine electrodes to increase capacitance for higher sensitivity in capacitative sensors [54]. Modified interdigitated electrode patterns have been used in single [55] and multilayer [56] capacitive sensing devices as well. Furthermore, IDEs help the overall device to be more compliant since a smaller area of the polymer surface is metalized compared to parallel electrodes found on 31-mode piezoelectric devices. P(VDF-TrFE) provides the best compromise between energy harvesting ability, durability in wearables, and human comfort. This material can convert energy from low frequency body motions into electricity, but also actuate and store energy as capacitors. Fabrication of the copolymer thin films with either multilayered structures or patterned electrodes have been researched separately for electromechanical transducer applications [53,57–60]. However, combining these two features is challenging, but can increase design flexibility. For example, mesh or grid-like flexible electrodes have been demonstrated to make stretchable electronics more mechanically robust [61]. These devices can adhere to the skin and be applied and removed hundreds of times without damaging the electronics.

1.6 Energy Harvesting and Storage Systems for Body Sensor Networks

Accurate monitoring and prediction of an individual’s health depends on having continuous and reliable data. Hence, body sensor networks (BSN), which consist of wearable sensors and computing devices, have been receiving more attention [62,63]. Additionally, BSNs that are self-powered (via energy harvesting) become “invisible” to the user by minimizing user intervention, which in turn motivates more widespread use. It is diﬃcult to determine, however, if a wearable device can be self-powered due to the wide variety of activities that people participate in and environments that they move through causing high levels of intermittency and variability in the power available for harvesting. For example, energy harvesting from motion depends on where the harvester is located on the body and what the person is doing, and energy from solar or thermal power depends mostly on the

8 environment. Factors like these cause self-power generation to vary considerably. The main sources of power for wearable energy harvesting are mechanical, solar, and thermal (Table 1.1). Thermoelectric generators (TEGs) produce power proportional to the temperature difference between the skin and the environment. Their efficiency depends on clothing and thermal coupling to the skin [64]. Me- chanical energy harvesters can generate power through the inertia of a vibrating proof mass attached to a transducer or direct force applied to a transducer [65]. The transducers are usually electromagnetic generators, piezoelectric materials, or triboelectric devices. Solar harvesters, on the other hand, are completely decoupled from the human body but depend on the environment (indoor or outdoor), ambient lighting conditions, and orientation of the harvester relative to the light source [66]. Radio-frequency (RF) energy is of great interest for wireless power transfer (WPT) systems, but the power per unit area available from ambient sources such as GSM tend to be very low [67]. The success of a wearable with fluctuating input power can generally be improved in three ways: (i) increasing the size, number, or type of energy harvesters, (ii) appropriately sizing the energy storage element, or (iii) controlling the energy consumption of the device. Assuming that the power consumption of the sensors cannot be changed but the power demand profile is known, minimal configurations of energy harvesting and storage elements can be determined based on average power levels and energy bounds [68]. This approach, however, is made difficult by the lack of future knowledge of human behavioral patterns. Experimental measurements of accelerations in the human body taken over a day have also been used to determine the available power associated with different activities and lifestyles [39], and state estimation methods were applied to predict the harvested power [69]. Maximum theoretical power of kinetic and thermal energy harvesters have been compared as a metric to determine which device is better for self-powered wearable devices, concluding that kinetic harvesters are ultimately capable of achieving higher theoretical power densities, but thermal generators are approaching their upper limit much more quickly [38]. However, a large set of human behavioral data has never been used to analyze the efficacy of different energy harvesting technologies for wearable devices.

9 Table 1.1. Harvested power for the diﬀerent energy harvesters.

Power Source Harvested Power

4µW/cm2 [70] Mechanical 30µW/cm3 [38] 330µW/cm3 (shoe inserts) [66] 30µW/cm2 [70] 10µW/cm3 [38] Thermal 15µW/cm3 (10°C gradient) [66] 10µW/cm3 (daily temperature variation) [66] 10µW/cm2 (indoor) [70] 10mW/cm2 (outdoor) [70] Solar 6µW/cm3 (indoor) [66] 15µW/cm3 (outdoor, cloudy) [66] 15mW/cm3 (outdoor) [66] Radio-frequency 0.1µW/cm2 [70]

1.7 Dissertation Outline

In chapter 2, the dynamic behavior of a multilayer relaxor ferroelectric terpolymer unimorph actuator is experimentally investigated. A linearized time-varying model is proposed, useful for practical design and control applications in haptics. The model reveals a new actuation mode that only a soft unimorph would be capable of without signiﬁcant a support structure: allowing the beam to vibrate at a high frequency and imparting the resonant kinetic energy onto another body by slowly varying the DC oﬀset. This approach is demonstrated by designing a rotary motor using EAP cantilever actuators. The functionality of the EAP actuators are demonstrated by integrating them into a haptic band to provide sensory feedback from a prosthesis. A rotary motor is also designed and used to estimate the output power of a single EAP actuator.

10 Chapter 3 explores the design, modeling, and analysis of chest strain energy harvesters that use rotary EM generators and piezoelectric PVDF films. The analyses consider the internal static friction of EM devices with high gear ratios, the soft tissue compliance of the human body, and power generation from slow, shallow breathing (i.e. low frequency and displacement) that occurs during most of the day. Experimental results with prototype devices showed that the EM generators produced power levels an order of magnitude higher than PVDF harvester. However, simulations revealed that PVDF could still harvest power at very low chest displacements while EM produced none due to static friction effects combined with soft tissue compression. In Chapter 4, an IDE model is derived to compare PVDF and P(VDF-TrFE) strain energy harvesters. A copolymer harvester with IDEs is found to be 1.8 times better than a PVDF with parallel plate electrodes (PPE). A new electrode design called interlaminar grid electrodes (IGE) is introduces that generates electric fields similar to IDEs, but are more mechanically robust to defects from fabrication or general use like PPEs. Finite element modeling is used to compare IDE and IGE electrode designs, and the limitations of the design when poling are discussed. Chapter 5 describes the fabrication of micron-sized electrode features on multilayer copolymer harvesters for flexible and robust wearable electronics. Capping layers address the problems associated with fabricating multiple layers with micron- scale features at the interface. The performance of alumina and PVA are compared as capping materials based on mechanical and electrical characteristics. In chapter 6, a database containing the behavioral data of a large, diverse population, called the Consolidated Human Activity Database (CHAD) [71], is used to estimate the amount of power that can be harvested from kinetic, thermal, and solar energy sources for different demographics. CHAD variables such as activity, location, and average temperature are used to estimate the time-varying power that is available for harvesting. These power profiles input to an energy harvesting and storage system model. The input power is converted to harvested power through the mechanical, thermal, and photovoltaic harvester models and losses due to human factors and electronics are applied. The remaining power is split between a supercapacitor and constant power consumption by the wearable device. Finally, the probability of success under self-powered operation based on Monte Carlo simulations is presented.

11 1.8 Key Contributions

• Using a linearized time-varying EAP unimorph actuator model that includes viscoelastic effects, a new haptic signaling mode, which combines low frequency oscillation of the bias deflection with a high frequency vibration component, is shown. This allows strong haptic signals to be sent from a soft, low mass unimorph actuator. A novel rotary motor that converts the oscillatory actuation of multiple cantilever soft actuators into shaft rotation is designed and analyzed. This device can be developed into a rotary actuator that is silent, precise, high torque, low speed, and has a high power density to fill many niche applications.

• The interlaminar grid electrode design is introduced which uses 33-mode and is more robust to fabrication defects through the used of a staggered grid structure and multiple layers. A fabrication process for multilayer P(VDF- TrFE) using capping layers is developed speciﬁcally for micron-scale electrode features. This enables not only the fabrication of IGEs, but other types of multilayer ﬂexible electronics as well using copolymer—a multifunctional material that is capable of actuation, sensing, and energy storage.

• A framework for translating human behavior into inputs for energy harvesters using a human activity database is developed. This type of real-world analysis using a large set of behavioral data to study wearable self-powered systems has not been conducted before. It quantiﬁes the impact of the burstiness (i.e. intermittency and irregularity) of human behavior and the environment on diﬀerent wearable energy harvesters.

12 Chapter 2 | Evaluation, Modeling, and Ap- plications of Electrostrictive Uni- morph Actuators

2.1 Introduction

The dynamics of the P(VDF-TrFE-CFE) unimorph actuators are explored in this chapter. These actuators are well-suited for wearable haptics for accessories and prosthetics due to their light weight, softness, and their ability to operate in the region of human tactile perception. Their behavior is ﬁrst experimentally investigated, then a model is presented that is useful for design and control using these devices. Finally, applications of the actuators is presented, where they were are to build a rotary motor and determine the output power and used for haptic feedback for a prosthesis.

2.2 Background and Initial Observations

Relaxor ferroelectric terpolymers are part of a class of EAPs that actuate primarily using electrostriction, meaning their strain is proportional to the square of the applied field. These polymers provide only positive strain because, as previously mentioned, their dipoles rotate from a random orientation (i.e an unpolarized state) to fully aligned with the electric field. Hence, the chain backbone orients itself perpendicularly to the electric field vector regardless of the sign of the vector.

13 Figure 2.1. (Top) Photo of Novasentis actuators epoxied to a base. The copper colored layer is active and the semi-transparent layer is passive. (Bottom) Magniﬁed view of the thickness of the actuator.

A photo of a Novasentis unimorph actuator is shown in the top image in Figure 2.1 and the bottom shows a cross-sectional view. The passive top layer is 50 µm thick polyether ether ketone (PEEK), but a temporary backing is shown in the image. Below that is a layer of adhesive and a stack of approximately 20-25 layers of 5 µm thick relaxor ferroelectric P(VDF-TrFE-CFE) terpolymer. Each layer had electrodes sputtered on both faces.

14 (a) (b) 1000 120

800 100

m] m] 7 7 80 600 60 400

40 Deflection [ Deflection Deflection [ Deflection 200 20

0 0 0 20 40 60 80 0 0.01 0.02 0.03 0.04 Time [s] Time [s] (c) (d) 1 Charge FRF 800 Measured 0.8 Deflection FRF 2 2 m] / = (825/150 )V

7 600 0.6 400 0.4

0.2 [ Deflection 200

0 0 0 100 200 300 400 500 0 50 100 150 Frequency [Hz] Voltage [V]

Figure 2.2. Experimental response of EAP cantilever tip: (a) displacement to a 100V step input and (b) a magniﬁed plot of the same response; (c) scaled charge and displacement frequency responses; (d) the hysteresis of the displacement under a triangle voltage wave with a 120s. period, compared to a parabola.

2.2.1 Viscoelasticity and Hysteresis

A laser vibrometer was used to measure the tip deflection of the EAP cantilever with applied voltage inputs. The response to a 100 V step input is shown in Figure 2.2(a)-(b). At first glance, the actuator seems to respond with a slow transient (Figure 2.2(a)), but looking at the first 0.04s. reveals a fast and underdamped initial rise (Figure 2.2(b)). The deflection shown in Figure 2.2(a) continues to rise very slowly for 90s. The nonlinearity in relaxor ferroelectric polymers is caused by electrostatic interactions and steric hindrances between polymer chains as the molecular conformation of the material changes to minimize potential energy [28,29]. This, along with the dynamics of the adhesive layer (Figure 2.1 bottom), could be the cause of the viscoelastic effect observed in Figure 2.2(a). Figure 2.2(c) shows

15 Figure 2.3. Polarization loop of a ferroelectric material before (A) and after (B) being converted to a relaxor ferroelectric via irradiation. Figure courtesy of Zhang et al. (1998).

normalized frequency responses of charge and deflection (resonance at 429Hz) with respect to input voltage. The trend shows that the two domains dominate at different frequency bandwidths. Displacement measurements (with a maximum of 825µm) show the device to be hysteretic (Figure 2.2(d)), which is common in this class of EAPs. Hysteresis effects for relaxor ferroelectrics are very low compared to ferroelectrics [26], therefore are neglected in the model. Figure 2.3 shows the difference in hysteresis between a ferroelectric and a relaxor ferroelectric [25]. The typical dielectric breakdown field for the terpolymer is greater than 400MV/m [26], but the applied field was kept well below that at about 30MV/m (or 150V for 5µm thick layers) because the actuator showed sparks if held at, for example, 200V (40MV/m) for a long time. One of the reasons is due to imper- fections in the fabrication process. The other is that the high curvature in the unimorph, associated with a high tip deflection, causes a reduction in thickness of the EAP layers due the Poisson effect and electromechanical coupling in the 31- and 32-modes. This increases the electric field in the material (due to the reduced distance between electrodes) and the chance of dielectric breakdown. Hence, the viscoelasticity prevented immediate failure by lowering the strain rate, which prevented the active layer from “over-thinning” too rapidly. Therefore, the actuator

16 1

0.9

0.8

0.7

0.6 Displacement (526.27m) Power (0.378W) 0.5 Current (8mA) Voltage (149.1V) 0.4

0.3

0.2

0.1

0 0 0.05 0.1 0.15 Time [s]

Figure 2.4. Experimental displacement, current, voltage and power step responses normalized by their maximum values shown in the legend. is able to accept higher voltages and provide larger output forces if the maximum curvature of the unimorph is constrained. For example, the actuator resting against a passive beam was able to vibrate the passive beam under a 250V sinusoidal input without experiencing dielectric breakdown because the passive beam limited the range of motion (and curvature) of the unimorph. These slow dynamic eﬀects not only impact the performance of the actuator, but can be used as a design parameter, so they are included in the model.

2.2.2 Power Dynamics

A Sawyer-Tower circuit was used to measure the charge of the EAP actuator. Frequency responses of charge and deﬂection are shown in Figure 2.2(c), where the amplitudes were normalized for better comparison. Both curves follow a similar

17 trend up to the first beam resonance. Current is the time derivative of charge, so this figure qualitatively shows the large improvement in power efficiency during resonance. It should be noted that the overall negative slope seen in both frequency responses is due to the additional impedance introduced by the Sawyer-Tower circuit. Figure 2.4 shows the normalized current, voltage, power and displacement during a step response, with their maximum values given in the legend. At 0.75s, the power is essentially zero, illustrating that very little power is required to maintain a force once the field has been established. This is a useful feature for applications such as remote presence, where a constant force must be provided to allow the sensation of holding a virtual object.

2.2.3 Current Haptic Technology

EAP actuators offer many advantages over haptic actuators that are used in current smart devices. Eccentric rotating mass (ERM) actuators and linear resonant actuators (LRA) are the most common types used today [72], shown in Figure 2.5. An eccentric center of gravity provides the vibration under rotation in an ERM. LRAs actuate a linear mass-spring system using magnetic fields. While LRAs can respond faster than ERMs, they must operate in a narrow bandwidth [73]. The advantages offered by EAPs over these actuators include lighter weight, faster response, higher frequency range, silent operation due to compliance, localized haptics (instead of vibrating the whole device), dynamic vibration patterns and the ability to conform to curved surfaces. EAP actuators require higher voltages (>200V), however they consume approximately the same amount of power as ERMs and LRAs.

2.3 Actuation Model

The actuator was modeled as an Euler-Bernoulli beam. The mode shapes for cantilever and pinned boundary conditions are used here, as they allow the system to be decoupled. Changes to the boundary conditions would require a recalculation of the mode shapes and complex boundary conditions can be handled by numerical approximation methods.

18 Figure 2.5. Eccentric rotating mass (top) and linear resonant (bottom) actuators. Image courtesy of Texas Instruments.

2.3.1 Model Derivation

A schematic of the beam model is shown in Figure 2.6. The strain in an electrostrictive material, proportional to the square of the electric ﬁeld, is given by the constituent equations (in Voigt notation) [74],

E 2 S1 = s T1 + M31E3 11 (2.1) D3 = 33E3 + 2M31E3T1

19 where S1 is the strain in the length direction, D3 is the electric displacement, E s11 is the compliance, T1 is the normal stress in the length direction, E3 is the electric field in the thickness direction, 33 is the dielectric permittivity and M31 is the electrostriction coefficient. The moment generated in the active layer of the unimorph with no external forces is analogous to a thermally expanding bimetallic strip. Hence, with a slight modification, the tip deflection can be expressed as [75],

c M V (t)2 δ (t) = c M E 2 = 1 31 tip 1 31 3 h2 2 (2.2) 3L bsbpYsYptstp (ts + tp) c1 = 2 2 22 2 2 (bsYsts) + bpYptp + 2bsbpYsYptstp 2ts + 2tp + 3tstp where V is the voltage, h is the thickness of a single terpolymer layer between each set of electrodes and L is the length. With the subscripts s and p representing substrate and active layer, respectively, bs and bp, ts and tp, and Ys and Yp are the widths, thicknesses, and length-direction elastic moduli (assumed to be transversely isotropic) of those layers, respectively. An initial guess for the value of M31 can be made by applying step voltages to the actuator, recording the steady-state tip 2 deﬂection and using equation (2.2). As shown in [26], M31 is proportional to E3 up to a certain extent and can be made a function of the average voltage depending on the required level of accuracy. From equation (2.2), the quasistatic moment can be described by, 2Y Iδ 2Y Ic M M(t) = tip = 1 31 V (t)2 (2.3) L2 L2h2 where YI is the bending stiﬀness of the entire beam actuator. Haptic devices will primarily use sinusoidal signals. Therefore, it is convenient to study the model in the frequency domain which requires it to be linearized. Using Taylor expansion on equation (2.3) yields,

4Y Ic M 2Y Ic M M(t) = 1 31 V V (t) − 1 31 V 2 (2.4) L2h2 avg L2h2 avg where Vavg is the mean of V (t). The total moment on the beam at any time t is given by [76],

∂2w(x, t) M (x, t) = YI + M(t)[H(x) − H(x − L)] (2.5) total ∂x2

20 % (3)

&(", #) $(#)

!(", #)

" (1)

% (3)

&(", #)

!(", #) $(#) " (1)

Figure 2.6. Free body diagram of the actuator in (top) cantilever and (bottom) pinned configurations. where M(t) comes from equation (2.4) and w(x, t) is the transverse deflection of the beam as shown in Figure 2.6. H(x) is the Heaviside function and is used to define a uniform moment over the beam and prevent M(t) from vanishing when spatial derivatives are taken. Equation (2.5) is used to develop the Euler-Bernoulli beam equation with damping [76],

∂4w ∂ ∂4w ∂w ∂2w YI + c I + c + ρA ∂x4 s ∂t ∂x4 a ∂t c ∂t2 (2.6) dδ(x) dδ(x − L) = M(t) − + f(x, t) dx dx

Here, cs is the Kelvin-Voigt damping coeﬃcient, ca is the viscous damping coeﬃcient,

I is the total area moment of inertia, ρ is the average density, Ac is the total cross sectional area, δ(x) is the Dirac delta function and f(x, t) is a distributed load on

21 the beam as shown in Figure 2.6. Using the parallel axis theorem, the total area moment of inertia and bending stiﬀness are given by,

0 0 I = Ip + Is 0 0 YI = YpIp + YsIs " # t 2 I0 = I + b t p + t − y p p p p 2 s n (2.7) " # t 2 I0 = I + b t s − y s s s s 2 n 2 Yptpbp (tp + 2ts) + Ystsbs yn = 2 (Yptpbp + Ystsbs)

0 0 where Ip and Is are the area moments of inertia of the active and substrate layers, respectively, about the neutral axis, yn, which is measured from the bottom of the beam. Ip and Is are the area moments of inertia of the active and substrate layers, respectively, about their centroids. The deﬂection can be deﬁned as a superposition of the product of two functions,

∞ ∞ X X w(x, t) = wn(x, t) = φn(x)qn(t) (2.8) n=1 n=1 where φn(x) are the mode shapes and qn(t) are the generalized coordinates. Follow- ing standard procedure in analytical beam vibrations, equation (2.8) is substituted R L into equation (2.6) and then multiplied by 0 φm(x)dx yielding,

∞ " X Z L ρAc φn(x)φm(x)dx q¨n(t) n=1 0 Z L Z L 0000 + csI φn (x)φm(x)dx + ca φn(x)φm(x)dx q˙n(t) 0 0 (2.9) Z L # 0000 + YI φn (x)φm(x)dx qn(t) 0 ∞ " # X Z L dδ(x) dδ(x − L) Z L = M(t) − φ (x)dx + f(x, t)φ (x)dx dx dx m m n=1 0 0

The mode shapes, which carry the boundary information, are given by the expression

22 below for a cantilever conﬁguration [77].

β x β x β x β x φ (x) = A sin n − sinh n − σ cos n − cosh n n n L L n L L (2.10) sin βn + sinh βn σn = cos βn + cosh βn

Here, An is a coeﬃcient that must be mass normalized and βn is given by the transcendental equation,

cos βn cosh βn = 1 (2.11) which is solved numerically. Pinned boundary conditions may be encountered more commonly in practice; their mode shapes are simply [77],

βnx φn(x) = An sin L (2.12) βn = nπ

The associated natural frequency for each βn is given by,

2 s βn YI ωn = (2.13) L ρAc

Under the pinned and cantilever boundary conditions the mode shapes are orthog- R L onal, i.e. 0 φn(x)φm(x)dx = 0 if m 6= n. These boundary conditions yield the kinetic energy inner product as,

Z L hφn(x), φm(x)iKE = ρAc φn(x)φm(x)dx = δmn (2.14) 0 where δmn is the Kronecker delta. Equation (2.14) is used to mass normalize the mode shapes by solving for An in equation (2.10) (or equation (2.12) for pinned beams). The potential energy inner product shares the following relation with the kinetic energy inner product for these boundary conditions,

Z L Z L 00 00 0000 hφn(x), φm(x)iPE = YI φn(x)φm(x)dx = YI φn (x)φm(x)dx 0 0 (2.15) 2 2 = ωn hφn(x), φm(x)iKE = ωnδmn

23 A location of interest at point x = Lδ can be deﬁned as,

δn(t) δn(t) = wn(Lδ, t) = φn(Lδ)qn(t) ⇒ qn(t) = (2.16) φn(Lδ)

which is where the beam deﬂection will be evaluated. The quasistatic moment given by equation (2.3) can be divided into components that separately model the underdamped vibrations and the viscoelastic dynamics,

n Xm M(t) = Mb(t) + Mi(t) (2.17) i=1

Here, Mb(t) is the moment that contributes to underdamped vibrations in Figure

2.2(b) and Mi(t), i = 1, . . . , nm, simulates the slow transient in Figure 2.2(a). The property below is useful for simplifying Dirac delta function integral found in equation (2.9), Z L dδ dφn (x − a)φn(x)dx = (a) (2.18) 0 dx dx Substituting equations (2.14), (2.15), (2.16), (2.17) and (2.18) into equation (2.9) yields an inﬁnite set of decoupled second-order diﬀerential equations of the form,

2 ¨ ωncsI ca ˙ 2 0 0 δn + + δn + ωnδn − (φn(L) − φn(0)) φn(Lδ)Mb(t) YI ρAc nm Z L (2.19) 0 0 X − (φn(L) − φn(0)) φn(Lδ) Mi(t) = φn(Lδ) f(x, t)φn(x)dx i=1 0

Using a ﬁnite number of mode shapes, equation (2.19) can be written in matrix form as, nm ¨ ˙ X Mδ + Cδ + Kδ + P Mi(t) + PMb(t) = F(t) (2.20) i=1 where M, C and K are diagonal matrices of size N × N, where N is the number of mode shapes used. The vectors δ, P and F are of length N. The matrix M, in this

24 case, is an identity matrix and the elements of δ, K, C, P and F are listed below.

δn = δn 2 K(n,n) = ωn 2 ωncsI ca C(n,n) = + YI ρAc (2.21) 0 0 Pn = − (φn(L) − φn(0)) φn(Lδ) Z L Fn = φn(Lδ) f(x, t)φn(x)dx 0

An examination of equations (2.4) and (2.17) shows that the moment can be expressed as,

nm ! Mavg X M(t) = µ + µ (2V (t) − V ) V b i avg avg i=1 2Y Ic M M = 1 31 V 2 (2.22) avg L2h2 avg n Xm µb + µi = 1 i=1 where µb and µi are moment weighting parameters. First order diﬀerential equations are used to approximate the dynamics of each moment contribution,

˙ 1 µbMavg Mb(t) + Mb(t) = VL(t) τb τbVavg ˙ 1 µiMavg Mi(t) + Mi(t) = VL(t) τi τiVavg (2.23)

for i = 1, . . . , nm

VL(t) = 2V (t) − Vavg

Here, τb and τi are time constants, and used as tuning parameters along with µb and

µi. An equivalent electrical circuit of equation (2.23) can be described as a voltage input circuit with nm + 1 parallel cascaded branches, each containing a resistor and capacitor in series. The summation of charges across all of the capacitors would be the output. The charge buildup across nm + 1 capacitors provides a sensible analogy for the moment because the reorientation of molecular chains in diﬀerent

25 regions of the polymer act over different time scales, hence the domains essentially have different electrical time constants. Even with randomly distributed domain sizes, the total strain across different samples was observed to be about the same, hence this modeling method is appropriate.

If Vavg is a function of time, equations (2.20) and (2.23) deﬁne a linearized time-varying system that governs this actuator,

VL(t) = 2V (t) − Vavg(t)

nm ¨ ˙ X δ(t) = −Cδ(t) − Kδ − P Mi(t) − PMb(t) + F(t) i=1 ˙ 1 2µbY Ic1M31 Mb(t) = − Mb(t) + 2 2 Vavg(t) VL(t) τb τbL h (2.24) ˙ 1 2µiY Ic1M31 Mi(t) = − Mi(t) + 2 2 Vavg(t) VL(t) τi τiL h

for i = 1, . . . , nm

w(Lδ, t) = 11×N δ ˙ w˙ (Lδ, t) = 11×N δ where 11×N is a horizontal vector of ones with N elements.

2.3.2 Point Force and Mean Power

If a point force is applied at location x = LF , then f(x, t) = F (t)δ(x − LF ) and the elements of Fn in equation (2.21) become,

Z L φn(Lδ)F (t) δ(x − LF )φn(x)dx = φn(LF )φn(Lδ)F (t) (2.25) 0

This is used to apply damping at the tip to evaluate the power by setting Lδ = L and using the expression,

F (t) = Fext(t) − ctipw˙ (Lδ, t) (2.26)

26 Table 2.1. Parameter values for EAP actuator.

Parameter Value

ρ 1270kg-m−3 L 8.8mm

bp 9.8mm

bs 12.5mm h 5µm

tp 190µm

ts 50µm

Yp 0.42GPa

Ys 3.6GPa

where Fext(t) represents other external forces and ctip is the tip damping. Mean power can be calculated by,

2 Pmean = mean ctip (w ˙ (Lδ, t)) (2.27)

2.3.3 Time-Varying Simulation Method

The time-varying simulation of equation (2.24) was done by discretizing the total simulation time into segments ∆ti, which are larger than the simulation time step size, and using the mean Vavg(t) of each time segment ∆ti as a constant for that segment, i.e. Vavg(t) = mean{Vavg(t): t ∈ ∆ti}∀t ∈ ∆ti. The system was simulated for time ∆ti and ﬁnal values of the state variables became the initial conditions for the next time segment ∆ti+1. Since the time-varying parameters are only found in the input matrix of the state-space model in equation (2.24), the eigenvalues do not change and this system remains stable in every case that the time-invariant system is stable.

27 1000

900

800

700

m] 600 7

500

400 Amplitude [ Amplitude 300

200

100

0 0 10 20 30 40 50 60 70 80 90 Time [s]

Figure 2.7. Simulation of 100V step input compared to experiment. For step responses, V (t) = Vavg(t), hence VL(t) = Vavg(t).

2.4 Results and Discussion

Experiments were carried out for the cantilever configuration. The experimental setup consisted of a voltage signal from a DAQ controlled by LabVIEW controlling the output of a voltage amplifier connected to the EAP actuator. The voltage of the output side of the amplifier was measured using a voltage divider circuit. A laser vibrometer was used to measure the tip deflection of the actuator. The bending stiffness was estimated by performing static deflection tests with a tip mass. The tip mass deflection tests indicated that the mode shape coefficients An had to be scaled by a factor of 1.2 because a small number of mode shapes were used. The value M31 was made a polynomial function of Vavg based on experiments and ranged from 6.25 × 10−18m2/V2 to 7.72 × 10−18m2/V2 for the simulation shown in Figure 2.9. The bulk parameters of the EAP actuator are given in Table 2.1.

28 12 V = 50V Experiment avg V = 75V Experiment 10 avg V = 100V Experiment

avg m/V]

7 V = 50V Model avg V = 75V Model 8 avg V = 100V Model avg

Transfer Function Amplitude [ Amplitude Function Transfer 2

0 0 50 100 150 200 250 300 350 400 450 500 Frequency [Hz]

Figure 2.8. Simulation of frequency response function compared to experiment at diﬀerent constant Vavg and the oscillation amplitude is 50V, i.e. V (t) = 50 sin 2πft + Vavg.

Figure 2.7 shows the same step response from Figure 2.2(a) along with the model result. Two moment equations, excluding Mb(t), were used in this simulation, i.e. nm = 2. The beam resonance was controlled by µb (0.105) and τb (0.28ms).

The parameters µi (0.06, 0.835 for i = 1, 2) and τi (0.015s, 2.25s for i = 1, 2) were estimated by trial and error to match the slow transient of the experimental step response, with priority being given to the initial rise since that will affect the dynamics at frequencies greater than one. For nm greater than two, a parameter estimation algorithm should be used, and will result in a better matching in Figure 2.7. The frequency response of the model and experiment are compared in Figure 2.8. Figure 2.9 shows time-varying simulations of the tip deflection under complex oscillation patterns and different initial conditions. If the system is started at steady-state, it matches well with the experiment overall, but has some amplitude

29 800 Experiment m] 600 7 Model

400

200 Deflection [ Deflection 0 0 1 2 3 4 5 6 7 8 9 10 Time [s]

400 m] 7 200

0 Deflection [ Deflection -200 0 1 2 3 4 5 6 7 8 9 10 Time [s]

Figure 2.9. Dynamic response (top) starting from zero initial conditions with V (t) = 50 sin 4πt + Vavg(t) and Vavg(t) = 25 sin πt + 75, and (bottom) starting from steady-state initial conditions at 75V with V (t) = 50 sin 2πt + Vavg(t) and Vavg(t) = 25 sin 0.5πt + 75.

error. This could be due to nonlinearities such as hysteresis. With zero initial conditions, the average simulation displacement increases more rapidly than the experiment. This parallels the error shown in Figure 2.7. Therefore, the result can be improved by using more moments to model the slow transient. Figure 2.10 shows a model-based estimation of mean output power using equation (2.27). Only the first 50Hz are shown, but the surface plot reaches a maximum of 0.62mW at resonance. This hints at an efficient way to operate the actuator in signaling functions such as notifications in phones and smart watches. While

oscillating V (t) at resonance, Vavg(t) can be used to control the average distance between the actuator and a body. Reducing the distance between the actuator and the body eﬀectively increases the average impedance on the actuator. This may be analogous to increasing tip damping and swinging over the maximum mean power (or in reference to Figure 2.10, controlling the steady-state deﬂection such

30 40

W] 7

10 Mean Power [ Power Mean

0 1 50 40 0.5 30 20 10 c [N-s/m] 0 0 Frequency [Hz] tip

Figure 2.10. Estimation of output power by applying tip damping to the actuator model and varying ctip to match impedance.

that ctip moves from 0 and 0.5). The kinetic energy of this low mass device can be increased by high frequency vibration and imparted onto the body using low frequency oscillation to send the strong haptic signals.

2.5 Rotary Motor

This idea of swinging back and forth over the maximum power was applied to the design of a rotary motor. A motor powered by these actuators has the potential to provide high accuracy, low speed, high torque, and silent rotation in a lightweight package. Additionally, such a motor can be made almost entirely from plastic which would make it ideal for assistive technologies and biomedical applications. A rotary motor was constructed using these actuators to evaluate their actuation capability. A similar device has been developed by Kornbluh et al. [78] using rolled electrostrictive actuators that deﬂect axially to oscillate a rotor that rotates a shaft

31 Figure 2.11. Rotary motor with ﬁve EAP actuators. The rotor (black) can be seen inside the outer housing (gray) resting on the actuators (brown). The largest cylindrical part of the motor has a diameter of 10.5cm and a height of 4.2cm. via a one-way clutch. Anderson et al. [79] also proposed an EAP-based design that used a stack of segmented dielectric membrane discs to produce a rotary motion in a manner similar to connecting rods rotating the crankshaft of an engine.

2.5.1 Design

The motor was designed to convert the oscillatory motion of several actuators into one-way rotation. This was accomplished by using a set of roller bearing clutches

32 (one-way clutches); one was mounted on the rotor which transferred the torque from the actuators to the output shaft uni-directionally and the other mounted on the support structure prevented the shaft from rotating in the opposite direction under high external loads. Figure 2.11 shows a photograph of the motor. Since the actuators were not attached to the rotor, a rotor return spring was used as shown in Figure 2.11. Initially, the motor structure included a stop to prevent the rotor fins from exerting too much force on the actuators, however it was discovered that the rotor fins needed to rest on the actuators in order to provide any output motion. This is because the stop was interrupting harmonic oscillation. The design was corrected by using an offset to allow the rotor to rest on the EAP actuators, however, since the rotor can separate from the actuators during operation so it is not a linear oscillating device. Under external torque, the actuators were observed to be in constant contact with the motor.

2.5.2 Performance

The motor, assembled with five actuators, was torque tested under a 150V (peak- to-peak) square wave pattern. Torque was applied by attaching different masses on a string wrapped around the output shaft. During the test, the position of a marker on the string was recorded using photographs. The time of each image was also recorded. Using the position and time information, the speed was determined at different torques. The rotor resonance frequency under zero load was observed to be about 10Hz. Due to thermal and nonlinear effects, and short lifespan of these actuators (because they were fabricated by hand), their performance varied between tests. For example, when the actuators were “warmed-up” after a few runs, their performance changed. The top of Figure 2.12 shows some typical torque versus speed curves. The maximum output power, calculated by torque times speed, was found to be 34.6µW at 10Hz. The torque test was repeated with different numbers of actuators with the results shown on the right side in Figure 2.12. The friction in the testing rig and also the friction in the motor itself was significant compared to the output torque. Therefore, the output power of the motor is given by,

Pm = nPact − Pv(ωm) − Pc (2.28)

33 350 35 9 Hz 300

10 Hz 30 W]

N-m] 11 Hz

250 7 7 25 200

Power [ Power 20 Torque [ Torque 150

100 15 0.05 0.1 0.15 0.2 0.25 0.05 0.1 0.15 0.2 0.25 Rotation Speed [rad/s] Rotation Speed [rad/s]

250 25 4 EAPs 3 EAPs 20

200 W]

N-m]

7 7 15 150

Power [ Power 10 Torque [ Torque

100 5 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 Rotation Speed [rad/s] Rotation Speed [rad/s]

Figure 2.12. Motor torque and power vs. speed (top) using five actuators for different frequencies and (bottom) at 9Hz for different numbers of actuators. The length of the red line shows the power contribution of one actuator near the maximum power of the motor.

where n is the number of actuators, ωm is the motor rotation speed, Pact is the power contribution of a single actuator, and Pv(ωm) and Pc are power lost to damping and Coulomb friction. The bottom of Figure 2.12 shows the torque and power curves for the motor with diﬀerent numbers of actuators oscillating at 9Hz. Based on the trend of these curves, it can be assumed the maximum power is achieved somewhere around 0.094 rad/s. Using equation (2.28), and assuming that Pv(ωm) and Pc are the same for both curves in the bottom power plot of Figure 2.12 at

ωm = 0.094rad/s, the upper bound on the maximum power of one actuator can be estimated to be about 8.87µW based on the drop in power from deactivating one actuator. This is shown by the length of the red line in Figure 2.12. The lower bound on the maximum power is the peak power of 34.6µW divided by 5 actuators which is 6.92µW. This gives the EAP actuator a maximum power density that is in

34 between 0.267-0.342W/g (based on the measured mass of the active layer) in the unimorph conﬁguration, which approaches the power density of electric motors.

2.5.3 Discussion

Unlike conventional motors, this rotary motor operates via impact forcing made possible due to its compliance. This operational mode may be able to generate higher kinetic energy at lower frequencies, which is useful for high torque, low speed applications. As the ratio of active material mass to total motor mass approaches 1, the motor reaches power densities similar to that of electric motors. High torque and low speed motors typically cannot be achieved on electric motors without a gearbox, which adds mass and consumes space. This motor design provides a way to use soft actuators to ﬁll this niche. Generally, impacts are avoided in oscillating systems due to wear and fatigue, but the “soft” nature (i.e. low inertia and high compliance) of these actuators and the low frequency of operation helps to ease those concerns. The “softness” also provides a high coeﬃcient of restitution, meaning that little energy is lost during an impact. Furthermore, the friction in the motor can be reduced by using a clutch made of active material that functions on the same electrical input as the actuators, instead of the passive mechanical clutches being used in this design.

2.6 Haptic Band for Prosthetic Feedback

The actuators were also implemented into a foot prosthesis to provide balance information to the user. Figure 2.13 shows the system. Three force sensitive resistors (FSRs) were used to calculate the roll angle of the foot against the ground. Based on the measurements, the corresponding terpolymer actuators in the haptic band would vibrate to indicate the direction of tilt. The objective was to allow a person with a prosthetic foot to regain the sense of balance that is generally conveyed through pressure at bottom of the foot. The user would have to get accustomed to this type of sensory feedback via neuroplasticity. The system provides relatively strong feedback, but the vibrations cannot always be felt equally well on all parts of the body due to the diﬀerences in impedance (caused by soft tissue compliance) in diﬀerent areas of the human

35 Buckled strap

Haptic Worn around thigh band Actuator

Flex connector Battery + Voltage Prosthetic booster foot EAP1

EAP2 FSR1

FSR2 EAP3

FSR3 EAP4

Haptic band

Figure 2.13. A haptic feedback system for a prosthetic foot using force sensitive resistors (FSRs) to calculate balance information and using a haptic band made of EAP actuators to convey that information to the user.

body. The advantage of using EAPs is that the vibration frequency can be easily changed based on requirements. Additionally, designers can devise ways of adding adjustable masses to the buckled strap on top of the actuator band to operate closer to resonance and intensify the vibrations. This non-invasive, detachable solution can be used on any body part with relatively minor design adjustments.

36 Chapter 3 | Modeling and Design of Elec- tromagnetic and Piezoelectric Chest Strain Energy Harvesters Including Soft Tissue Eﬀects

3.1 Introduction

This chapter explores the design, modeling, and analysis of wearable chest strain energy harvesters that use electromagnetic generators and piezoelectric polymers including the eﬀects of soft tissue compliance. Electromagnetic generators are shown to produce more power than piezoelectric polymers during deep breathing. During shallow breathing, however, the polymer harvester performs better because static friction and soft tissue compression limit power generation in the electromagnetic harvester.

3.2 Harvester Types

Two different types of chest strain harvesters were constructed. The first used a single EM generator that rotated with the expansion and contraction of the chest, as shown on the left in Figure 3.1. EM generators have a very high electromechanical coupling, so they have the potential to harvest large amounts of power from breathing. However, the combined effects of static friction, backlash, and soft tissue

37 EM Harvester

PVDF Harvester

Electronics

Figure 3.1. Prototypes of EM harvester (left) and PVDF harvester (right). compression prevent the devices from harvesting signiﬁcant energy from the small chest displacements that occur during normal breathing. In other words, shallow 29 breathing does not produce enough force to overcome static friction in the gear train of the generator in many cases. Additionally, the soft tissue, which acts like a soft spring, reduces the available force. A second type of chest strain energy harvester was constructed using PVDF, shown on the right in Figure 3.1. This device placed a long, narrow PVDF strip in series with a passive material in two loops around the chest. Placing the materials in series enables the use of more PVDF material and control over the force acting on the PVDF based on the stiﬀness of the passive material.

3.3 Derivation of the Electromagnetic Generator Model

The generator was an oﬀ-the-shelf servomotor (Futaba S3001) that was modiﬁed to remove the controller and mechanical stop, leaving a brushed DC motor and a gear train. The harvester used a cord wrapped around the chest to transmit the chest circumferential displacement and rotate the generator via a pulley. A return spring was used to rotate the generator backward during chest compression, generating power during both inhale and exhale. The electromagnetic energy harvester model is shown in Figure 3.2(a). Soft tissue compliance, return spring, and pulley were added to create the full harvester model shown in Figure 3.2(b). Figure 3.2(c)

38 shows the compression belt and harness used to attach the harvester around the chest with harvester cord that connects to the pulley. Figure 3.2(d) shows the components of the harvester assembly. The EM generator shown in Figure 3.2(a) is described by,

¨ ˙ kp (θl(t) − θ(t)) = Jθ(t) + KT I(t) + Tf θ(t) (3.1)

where θl(t) is input rotation to the generator, J is the moment of inertia of the ˙ generator, KT is the motor torque constant, I(t) is the current, Tf θ(t) is the

friction, and θ(t) is the shaft angle. The drivetrain torsional spring, kp, models compliance and backlash in the plastic gears and output shaft. The electrical dynamics, simpliﬁed by neglecting the inductance, are,

˙ V (t) = KEθ(t) = (Rm + R) I(t) (3.2)

where V is the generated voltage, KE is the motor voltage constant, Rm is the internal resistance of the motor, and R is the load resistance. Combining equations (3.1) and (3.2) yields the governing equation for the EM generator.

¨ KT KE ˙ ˙ kp (θl(t) − θ(t)) = Jθ(t) + θ(t) + Tf θ(t) (3.3) Rm + R

A Stribeck friction model [80] is used:

" 2# θ˙(t) θ˙(t) θ˙(t) T θ˙(t) = (T − T ) exp − + T tanh 10 + bθ˙(t) (3.4) f s c ˙ ˙ c ˙ θf θf θf

˙ Here, θf is the Stribeck velocity [81], Tc is the Coulomb friction, Ts is the static friction, and b is the viscous friction coeﬃcient. The generator output voltage across the load is given by the equation below.

˙ KEθ(t)R VR(t) = (3.5) Rm + R

39 푥푙

푥 푘푠 푐

푅 푏푚 푅 푟푝 푚 푚 푘푚 푘푝 푘푝 Load Load 푉푅 퐽푝, 푟푝 푉푅 푅 푅

퐽, 푇푓, 퐽, 푇푓, 퐾푇, 퐾퐸 퐾푇, 퐾퐸 (a) (b) Return spring

Harvester cord Compression belt 6

Generator Pulley (c) (d)

Figure 3.2. Schematic of the rotary EM generator unit (a) and the energy harvester 16 with soft tissue compliance (b). Photos of a prototype EM chest strain energy harvester including the harness (c) and internal components of the harvester assembly (d).

3.3.1 Electromagnetic Harvester Model with Soft Tissue Com- pliance

The radial elasticity of chest soft tissue was modeled as a linear spring, represented by ks. Essentially, the displacement of the harvester cord, xc, due to the radial expansion of the chest transmitted through soft tissue can be simpliﬁed to an input lung displacement, xl through an equivalent spring, ks, that causes the displacement xc. Experimentally, the constant for this equivalent spring can be determined by wrapping a belt around the chest and measuring the force and circumferential

40 displacement as the belt is tightened. The equation of motion for the harvester components around the generator is given by,

Jp ks(xl(t) + x0 − xc(t))rp = x¨c(t) + bmrpx˙ c(t) + kmrpxc(t) (3.6) rp where x0 is an initial displacement, rp is the radius of the pulley, Jp is the pulley inertia, bm is the damping of those components, and km is the return spring constant. Pre-stress can be applied to the chest in two ways: an initial displacement by tightening the harvester cord, or increasing soft tissue stiffness by wearing compressive clothing. The harvester cord and a compression belt are shown in Figure 3.2(c). Tightening the harvester cord is represented by the initial displacement, x0. Tightening the compression belt effectively increases the body compliance, ks. Therefore, this parameter represents the combined compliance of soft tissue and compressive clothing. The comfort of the user depends on the pre-stress, so there are bounds on how high x0 and ks can be. Equation (3.3), with θl(t) replaced by xc(t)/rp, is the second equation of motion for this system, xc(t) ¨ KT KE ˙ ˙ kp − θ(t) = Jθ(t) + θ(t) + Tf (θ(t)) (3.7) rp Rm + R and equation (3.5) gives the generated voltage across the load. Figure 3.2(b) shows that the cord only provides tension so we assume pretension ensures the cord does not have slack. We also assume that the pulley inertia, Jp, and the harvester damping, bm, are negligible due to the low weight and frequency. This simplifies equation (3.6) to,

ks xc(t) = xl(t) (3.8) km + ks and the term ks/(km +ks) acts as a scaling factor for the input displacement because some of it is lost in the soft tissue motion. Using equation (3.8), the simpliﬁed governing equation for a generalized EM harvester is, ks xl(t) ¨ KT KE ˙ ˙ kp − θ(t) = Jθ(t) + θ(t) + Tf (θ(t)) (3.9) km + ks rp Rm + R

41 3.4 Derivation of the PVDF Harvester Model

Figure 3.3 shows a schematic and 3D model of the fabricated PVDF harvester. The short edges of PVDF were attached to a piece of webbing such that the distance between the attachment points on the webbing was 1.01 times the length of the PVDF. This allowed for the PVDF to stretch to 1% strain before the webbing prevented it from stretching any further. The section containing the PVDF was attached in series with a passive material represented by the spring ki in the schematic. The dynamics of the PVDF with parallel electrodes can be found by starting with the constitutive piezoelectric equations (in the 1-direction),

E S1 = s T1 + d31E3 11 (3.10) T D3 = d31T1 + 33E3 where S1 is the strain, T1 is the stress, D3 is the electric displacement, E3 is the E electric field, s11 is the in-plane material compliance in the direction of strain, d31 is T the piezoelectric coefficient, and 33 is the dielectric permittivity. The superscripts E and T indicate that the parameters were measured under a constant electric field or constant stress, respectively. Energy methods can be used to derive the governing equations of the PVDF. The internal energy of a volume element is given by,

1 1 1 1 dU = S T + D E = sE T 2 + T E 2 + d T E (3.11) 2 1 1 2 3 3 2 11 1 2 33 3 31 1 3 and integrating over the volume yields the total energy,

" 2 2 # 1 E F 1 T V F V U = s11 + 33 + d31 bpLtp (3.12) 2 bptp 2 tp bptp tp where bp is the width of the polymer, tp is the thickness, F is the force acting on the area bptp to produce the stress T1, V is the voltage across the material thickness that produces the electric ﬁeld E3, and L is the length. From the energy, the charge can be calculated by taking the derivative with respect to voltage.

T ∂U 33bpL d31L Q = = V + F = CpV + Qgen (3.13) ∂V tp tp

42 푥푙

푘푠 Material represented by 푥푖 푘푖 PVDF

푘푖

푇 푥 푑33, 휖33, 푌푝 푐

Load 푉푅 Webbing acts as strain limiter

푅 PVDF

Figure 3.3. Schematic of the PVDF harvester (left) and 3D model of the prototype (right).

6 The second term in equation (3.13) is the generated charge, i.e. Qgen = d31LF/tp, T and the ﬁrst term excluding the voltage gives the capacitance, Cp = 33bpL/tp. The current across the PVDF can be found by diﬀerentiating equation (3.13),

dQ(t) T b L dV (t) d L dF (t) V (t) I(t) = = 33 p + 31 = (3.14) dt tp dt tp dt Rl

where Rl is the load resistance. In the frequency domain, the transfer function for the output voltage to the input force is giving by,

V0 d31RlLω = q (3.15) F0 T 2 2 (33bpRlLω) + tp

where V0 and F0 are the amplitudes of the sinusoidal force and voltage, respectively. And from this, the power for the circuit can be calculated using the formula below.

V 2 (F d Lω)2 R P = 0 = 0 31 l (3.16) R T 2 2 l (33bpRlLω) + tp

43 0.3 Hz 0.6 Hz 0.9 Hz 2 4 1 1 2

0 0 0

Voltage [V] Voltage -1 -2 -1 -2 -4 0 2 4 6 0 2 4 6 0 2 4 6

20 40 20 20 0 0 0 -20 -20 Rotation [deg] Rotation -20 -40 -40 0 2 4 6 0 2 4 6 0 2 4 6 Time [s] Time [s] Time [s]

Figure 3.4. Output voltage simulation (red) versus experiment (black) for the EM generator in response to sinusoidal input rotations (θl(t)) at 0.3, 0.6, and 0.9 Hz.

Maximum power is achieved when the load resistance matches the impedance of the PVDF capacitance. The optimum load is given by,

1 tp Ropt = = T (3.17) Cpω 33bpLω which can substituted into equation (3.15) to get the maximum voltage under a sinusoidal input. √ 2 F0d31 Vmax = T (3.18) 2 33bp Using equations (3.17) and (3.18), the maximum power can be found.

2 2 Vmax (F0d31) Lω Pmax = = T (3.19) Ropt 233bptp

Additionally, F0 can be deﬁned in terms of strain using F0 = S1Y11bptp, where Y11 is E T the elastic modulus of the polymer (i.e. the inverse of s11) and 33 must be replaced S T 2 with the dielectric permittivity at constant strain, deﬁned by 33 = 33 − d33 Y11.

44 3.4.1 PVDF Harvester Model with Soft Tissue Compliance

The wearable PVDF harvester is represented by three springs in series, as shown in Figure 3.3. Similar to the EM harvester, these springs were treated quasi-statically with dynamics only in the electrical domain. The equation for strain on the PVDF is given by, keq S1(t) = xl(t) (3.20) Y11bptp + keqL

where keq = kski/(ks + ki) and ki is the stiﬀness of the passive material.

3.5 Experiment and Validation

The EM generator and the PVDF material are the energy conversion elements of the chest strain energy harvesters. A series of experiments were performed to estimate the parameters and validate the model of the generator given by equation (3.3). Validation was also performed for the PVDF material model given by equation (3.16).

3.5.1 Electromagnetic Generator Model Validation

The torque from static friction, Ts, was measured by incrementally adding weight to a pulley attached to the generator until it began to move. The torque constant was estimated using a static torque test, where an extension arm was attached to the generator and voltage was applied to run it as a motor. The extension arm applied a force to a scale to produce torque on the generator shaft. The torque constant was calculated using,

mgr K = m (3.21) T I(t)

where m is the scale’s mass reading, g is the acceleration of gravity, and rm is the length of the extension arm. The viscous damping coeﬃcient and moment of inertia were estimated from the angular velocity response (recorded with a camera) when the generator was run as

45 a motor under a step voltage. It follows the equation,

Vs(t) ¨ ˙ KT I(t) = KT = Jθ(t) + bθ(t) (3.22) Rm which is a linear version of equation (3.1) (i.e. only viscous friction) with voltage input instead of rotation. Here, Vs is the applied step voltage. The solution to equation (3.22), given below, was used to estimate b and J.

K V (t) b θ˙(t) = T s 1 − exp − t (3.23) Rmb J

Finally, a manual frequency response test was conducted. The generator was excited by a shaker at different frequencies, and the output voltage was recorded. The static friction in the device produced flat sections in the sinusoidal response, so a fast Fourier transform (FFT) could not be used. Hence, the amplitudes were manually recorded. A linear version of equation (3.3) (i.e. a model with only viscous friction) was used to curve fit the frequency response amplitude data using

MATLAB cftool to determine KE and kp.

The value of kp was used as a starting guess and changed to match high frequency dynamics that were observed in the output voltage of Figure 3.4. The estimation of the friction and damping coefficients, Ts, Tc, and b, was improved by minimizing the sum-squared error, n X 2 ss = (Vsim,i − Vexp,i) (3.24) i=1 using the MATLAB command fminsearch on the experimental data. Here, Vsim,i are Vexp,i are the simulated and measured output voltages of the generator, respectively, for n points in the time-domain data at frequencies of 0.3, 0.6, and 0.9Hz. The average error of all three frequencies is minimized, and then the estimated parameters were scaled based on the known static friction parameter value. The electromagnetic generator model parameters were measured using static and dynamic testing to produce the values given in Table 3.1. Figure 3.4 shows simulations of the generators at different frequencies compared to the experiment. The results show good matching between theory and experiment, including the effects of stiction and are shown in Table 3.1. The average power output at varying loads was measured under a sinusoidal input rotation. The model was simulated

46 14

4 Avg. Power [mW] Power Avg.

0 0 100 200 300 400 500 600 700 800 900 1000 Resistance [ ] 120

100

W] 80

40 Max. Power [ Power Max. 20

0 1 2 3 4 5 6 7 8 9 10 11 Resistance [M ]

Figure 3.5. EM generator average power (top plot) measured (circles) and simulated (lines) versus the load resistance under sinusoidal input rotation with frequencies of 0.3, 0.6, and 0.9Hz shown using dark, medium, and light colored lines, respectively. PVDF peak power (bottom plot) measured (circles) and simulated (lines) versus the load resistance under 0.17% strain amplitude sinusoidal input with frequencies of 0.5, 0.75, and 1 Hz shown using dark, medium, and light colored lines, respectively. using the measured input and the results are shown to match well in top plot of Figure 3.5.

3.5.2 PVDF Model Validation

The parameters of the PVDF material, obtained from the manufacturer (Measure- ment Specialties, Inc.), and dimensions are shown in Table 3.1. A sheet of PVDF was stretched under a sinusoidal input strain at varying load resistances and the

47 Table 3.1. Model parameters.

Parameter Value

J 28.4 kg cm2 b 165 kg cm2 s−1

Ts 9.30 N cm

Tc 3.24 N cm −1 KE 0.902 V s rad −1 EM KT 10.4 N cm A −1 kp 170 N cm rad

Rm 8 Ω

rp 1.1 cm −1 km 990 N m

tp 28 µm L 14.6 cm

bp 6.6 cm T 113 pF m−1 PVDF 33 Y11 3 GPa −1 d33 -33 pC N −1 d31 23 pC N

power was recorded. The experimental results match the model well as shown in the bottom plot of Figure 3.5. Since shallow breathing is being investigated, a low input strain of 0.17% (i.e. S1 = 0.0017 then F0 = 9.42N) was used for the experiment.

48 Table 3.2. Breathing energy harvester prototype power levels.

Transducer Input Displacement Output Power

EM1 Deep breathing ∼25mW (peak) PVDF1 Deep breathing ∼1mW (peak) 0.76µW/cm2 (peak, with PDMS2 [33] Deep breathing ∼7-9cm2 active area) PZT-5A [37] Normal breathing4 64µW (mean) PVDF3 [30] Normal breathing4 <1µW (mean) EM [37] Normal breathing4 0.56mW (mean) EM3 [31] Normal breathing 3.1µW (peak)

1Prototype in this work. 2Triboelectric device. 3Uses respiratory airﬂow. 4Mechanically simulated breathing.

3.6 Power Output

Since wearable energy harvesters depend heavily upon human factors (i.e. variability in the strength of the individual, soft tissue stiffness, and ergonomics), the input power to the harvester varies greatly in reported results making it difficult to compare different designs and transducers. However, breathing motion is relatively similar among different kinds of people and provides a good basis for comparison of wearable harvesters that may have been tested on very different body types. Table 3.2 provides measured output power of the EM and PVDF chest strain energy harvester prototypes and breathing energy harvesters in literature, including some that function on respiratory airflow. The EM harvester has a static friction torque of 9.3N-cm. For a 1cm radius pulley (a reasonable size for a wearable device), the EM harvester needs 9.3N to overcome static friction, based on the parameter Ts. Under a similar amount of force, a 14.6cm × 6.6cm PVDF film can generate 97µW at 1 Hz. The static friction torque, however, allows the EM harvester to store energy and suddenly release it

49 when the breakaway force threshold is reached to produce high velocities leading to high peak power. On the other hand, the weight of the EM generator is 45g (not including the harvester housing, pulley, cord, and return spring) while the weight of the PVDF ﬁlm is only 0.46g.

3.7 Simulation of Soft Tissue Eﬀects

Simulations of EM and PVDF harvester prototypes are shown in Figure 3.6 and Figure 3.7, respectively. In order to mimic steady breathing, the simulations use the same shallow breathing input displacement of 0.5cm at 0.3Hz. The surface plot in Figure 3.6 shows the average power generated by the EM harvester model with soft tissue and return spring stiffnesses, and an optimum load of 8Ω. The soft tissue stiffness is estimated as ks = Eswb/2π, where Es is soft tissue modulus and wb is the belt width. A region of zero power generation exists for high return spring stiffness and low soft tissue modulus. Plateaus that produce around 0.3mW and 0.6mW, and their example time responses, are indicated by A and B, respectively. The angular velocity responds via sharp impulses as it breaks away from the static friction. Since voltage is proportional to angular velocity in EM devices, the high angular speed after breaking away from static friction is beneficial to the device. When the soft tissue modulus is higher, there are more impulses because less input displacement is lost to soft tissue compression. The responses shown in A and B mimic the measured responses in [36] which examined a similar generator. PVDF is a linear elastic material and generates power at all values of ks and Es as shown in Figure 3.7. The power produced by the PVDF harvester, however, is orders of magnitude lower than the EM harvester. Power output can be increased by proportionally increasing the area of the PVDF and decreasing the thickness. For example, reducing the thickness of the PVDF from 28µm to 5µm and increasing the width to 30cm can generate 0.153µW of power at an Es of 10kPa (female torso soft tissue modulus [82]) where it previously generated 0.017µW in Figure 3.7. Higher strains are induced in thinner films of PVDF because they match soft tissue stiffness more closely. Furthermore, using a large backing layer (such as the wide belt shown in the 3D model in Figure 3.3) can effectively increase soft tissue stiffness and improve the performance of both devices. Micro-generators can also be used in EM harvesters to lower static friction,

50 0.5

0.8 0 Angle[rad] 0.6 d /dt -0.5 Input

0.4 6 8 10 12 14 Time [s]

MeanPower [mW] 0.2 0.5

0 1400 0 1200 60 50 1000 40 30 Angle [rad] d /dt 800 20 -0.5 Input k [N/m] 10 m 600 E [kPa] 0 s 6 8 10 12 14 Time [s]

Figure 3.6. EM harvester prototype simulated mean power versus return spring constant, km, and soft tissue modulus, Es. Plots A and B on right show the corresponding EM harvester time responses. however they would still require signiﬁcant support structures. Additionally, since EM power generation is proportional to velocity, static friction can be used as a clutch that releases the device when a force threshold is exceeded. The PVDF harvester form factor is much more ergonomic than EM devices and can be more easily integrated into clothing to generate electricity from all body motions.

51 0.6

0.5

W] 0.4

0.3

0.2

Mean Power [ Power Mean 0.1

0 10000 60 5000 40 20 k [N/m] 0 0 E [kPa] i s

Figure 3.7. PVDF harvester prototype simulated mean power versus passive material stiﬀness, ki, and soft tissue modulus, Es, for a 70 cm × 3 cm PVDF strip.

52 Chapter 4 | Model-Based Analysis of P(VDF- TrFE) Energy Harvesters with Interdigitated Electrodes

4.1 Introduction

Wearable self-powered electronics require thin, light, and flexible bio-compatible transducers. The piezoelectric polymer, P(VDF-TrFE), is well-suited to fill this need. Through model-based analysis, it is shown that P(VDF-TrFE) can outperform PVDF under the same forcing, which is related to comfort in a wearable device. A new electrode design that increases efficiency over a parallel plate electrode (PPE) harvester while being more resistant to defects by employing a multilayer design is proposed and analyzed.

4.2 P(VDF-TrFE) Energy Harvesters in d33 Mode

Piezoelectric polymers such as PVDF and its copolymers are ideal for wearable devices and textile integration since their mechanical properties are closer to textiles than piezoceramics due to their low denisty (1780kg/m3 compared to 7600kg/m3 for PZT), low bending stiffness, and low modulus (1-3GPa [83] compared to approximately 40GPa for PZT fibers [84]). The PVDF copolymer, P(VDF-TrFE), is compared to the PVDF homopolymer as a wearable energy harvester. Copolymer has lower stiffness and dielectric permittivity than PVDF, as shown in Table 4.1.

53 Branches Rails Bond pads 3 (a) 2 1 Harvesting area + - + 1 (b) 3 2 + - + Dead zone s w + e - e +

(c) tp + - + Figure 4.1. (a) Photo of a typical IDE pattern where the harvesting area is the portion of the device that generates voltage when stretched and the rails that connect all of the branches are on the left and right of the harvesting area, (b) schematic of IDE across three electrodes showing the material (white), electrodes (red), and electric ﬁeld lines (green), and (c) a simpliﬁed schematic for modeling. The dead zone under the electrode generates a negligible amount of electricity when the material is stretched axially. The circle in the coordinates represent an arrow pointing out from the page.

Interdigitated electrodes (IDE), shown in Figure 4.1(a), allow the poling and strain directions to align (i.e. using d33 mode instead of d31) resulting in better electromechanical eﬃciency. Each comb-like set of electrodes carry voltages of opposite polarity, causing most of the electric ﬁeld to be oriented in-plane. The rails connect all of the branches to the bond pads where electronics and energy storage are connected. The direction of stretching is in-plane and perpendicular to

54 Table 4.1. Material properties of PVDF and P(VDF-TrFE) from TE Connectivity and Piezotech Arkema, respectively.

Property PVDF P(VDF-TrFE) Units

T Dielectric permittivity (33) 110.7 82.3 pF/m

Elastic Modulus (Y33) 3 1.2 GPa

Piezoelectric 33 coeﬃcient (d33) -33 -30 pC/N

Piezoelectric 31 coeﬃcient (d31) 23 11 pC/N

Thickness (tp) 4 4 µm

Width (bp) 2 2 cm Length (L) 7 7 cm

branches (i.e. 3-direction). Copolymer can be poled simply by the application of heat and electricity. PVDF, on the other hand, requires the extra step of stretching which can be very complicated for a micron-sized electrode pattern. Figure 4.1(b) shows the cross-sectional view of a typical IDE pattern. The green lines show the path of the electric field, which align with the direction of strain through most of the material. There are dead zones under every pair of electrodes that do not generate power because the net vertical electric field is zero due to symmetry and the horizontal field is negligible. Also, the stiffness of the electrodes reduce the strain experienced by the piezoelectric material in that region. The simplified IDE model shown in Figure 4.1(c), originally proposed by Hagood et al. [85], is used here. This approach is justified for thin films with a high aspect ratio of electrode spacing to copolymer thickness (se/tp) which produce straighter electric field lines. Finite element analysis has been used to show that IDEs produce at least 80% of their theoretical maximum power when the aspect ratio is greater than or equal to 4 [86]. The output voltage is proportional to the electrode spacing, so an efficient harvester that produces low voltages would require very thin films.

55 4.2.1 Modeling of Interdigitated Electrodes

The constitutive piezoelectric equations in the 3-direction are,

E S3 = s T3 + d33E3 33 (4.1) T D3 = d33T3 + 33E3

where S3 is the strain, T3 is the stress, D3 is the electric displacement, E3 is the E electric field, s33 is the compliance (inverse of E33), d33 is the piezoelectric coefficient, T and 33 is the dielectric permittivity. The 3-direction is the poling direction and the superscripts E and T indicate that the parameters were measured under a constant electric field or constant stress, respectively. Following a procedure similar to Chapter 3, energy methods are used to derive the IDE model. The simplified model in Figure 4.1(c) can be divided into two parts: the active zone that has parallel electric field lines, and the passive area (i.e. dead zone) under the electrodes. The internal energy for each of those segments can be written as,

1 1 1 E 2 1 T 2 dUac = S3T3 + D3E3 = s33T3 + 33E3 + d33T3E3 2 2 2 2 (4.2) 1 1 dU = S T = sE∗T 2 ps 2 3 3 2 33 3

where Uac is the energy of the active zone, Ups is the energy of the dead zone, E∗ E s33 is the compliance of the electroded section which is lower than s33 due to the stiﬀness contribution of the electrode. Integrating both energies over their respective volumes and summing them yields the total energy,

" 2 2 # 1 E F 1 T V F V U = s33 + 33 + d33 nsebptp 2 bptp 2 se bptp se (4.3) 2 1 E∗ F + s33 (n + 1)webtp 2 bptp

where bp is the width of the polymer, tp is the thickness, se and we are the spacing and width of the IDEs (shown in Figure 4.1(c)), n is the number of electrode sets

(i.e. length of the polymer is L = n(se + we)), F is the force acting on the area bptp

to produce the stress T3, and V is the voltage acting on the length se to produce

56 the electric ﬁeld E3. The charge can be calculated by taking the derivative with respect to voltage as shown below,

T ∂U n33bptp Q = = V + nd33F = CpV + Qgen (4.4) ∂V se

where the ﬁrst term excluding the voltage gives the capacitance, i.e. Cp = T n33bptp/se and second term in equation (4.4) is the generated charge, i.e. Qgen =

nd33F . The open circuit voltage can be found by dividing these two terms.

Qgen d33se Voc = = T F (4.5) Cp 33bptp

Equation (4.5) shows that the output voltage can be modified by changing the electrode spacing, which is practically simpler than PPEs where the thickness of the material must be modified to change the output voltage. This is an important consideration when designing the power conversion electronics for these devices. The dynamics of IDEs can be derived by connecting the harvester to a load resistor. The current across the copolymer can by found by differentiating equation (4.4), which gives the equation for the circuit current,

T dQ(t) n33bptp dV (t) dF (t) V (t) I(t) = = + nd33 = (4.6) dt se dt dt Rl

where Rl is the load resistance. The transfer function for the output voltage to the input force is,

V0 nsed33Rlω = q (4.7) F0 T 2 2 (n33Rlbptpω) + se

where V0 and F0 are the sinusoidal force and voltage amplitudes, respectively. The power for the circuit can be calculated by,

V 2 (F ns d ω)2 R P = 0 = 0 e 33 l (4.8) R T 2 2 l (n33Rlbptpω) + se

The maximum power is achieved when the total capacitance of the IDEs is impedance matched to the load. The optimum load is given below.

1 se Ropt = = T (4.9) Cpω n33bptpω

57 Maximum voltage under a sinusoidal input can be found by substituting equation (4.9) into equation (4.7). √ 2 F0d33se Vmax = T (4.10) 2 33btp The maximum power can be found using equations (4.9) and (4.10).

2 2 Vmax (F0d33) nseω Pmax = = T (4.11) Ropt 233bptp

4.2.2 Model Based Comparison of PVDF and P(VDF-TrFE)

Since user comfort is one of the prime motivations of investigating piezoelectric polymers as energy harvesters, a useful ﬁgure of merit for the comparison of PVDF and P(VDF-TrFE) would be power produced per unit area under the same input force. Figure 4.2(a) shows that the power output of copolymer with IDEs, plotted using equation (4.8) using 2N of input force amplitude, is about 1.8 times higher than PVDF with parallel plate, but the optimal load is also two orders of magnitude higher. The optimal load, however, can be controlled by changing the ﬁlm width

(bp) and length (which proportionally changes n), as shown by equation (4.9). When comparing both devices with IDEs, copolymer is able to produce more power than PVDF at the optimal load under the same input force (Figure 4.2(b)). The parameters for PVDF and copolymer given in Table 4.1. At 2N, a reasonable force level for wearable harvesters, copolymer ﬁlm with the dimensions in Table 4.1 is strained by about 2% and produces approximately 100µW. The optimal load can be reduced by increasing the ﬁlm area while maintaining the same length to width ratio, and still producing the same amount of power. For example, increasing the area by 102 reduces the optimal load by the same amount while still producing 100µW. This can be used to optimize the power conversion electronics.

4.2.3 Multilayer Interlaminar Grid Electrodes

We investigate another electrode design based on IDEs called interlaminar grid electrodes (IGEs). IGEs borrow design aspects from both IDEs and PPEs. IGEs align poling and strain directions by the use of staggered electrodes, similar to

58 × 10-2

8 ) 2 7 (a)

6 (W/m 5 4 3 2

1 Power Power per unit area 0 6.0 6.5 7.0 7.5 8.0 8.5 9.0 log (R ) × 10-2 10 l

8 ) 2 7 (b) 6 5 4 3 2

1 Power per Power unit per area (W/m 0 7.0 7.5 8.0 8.5 9.0 log10(Rl)

Figure 4.2. PVDF (solid) and copolymer (dashed) power output per input force at diﬀerent load resistances under 2N input forcing amplitude. Comparison of (a) PVDF with PPEs and copolymer with IDEs and (b) both PVDF and copolymer with IDEs. The dark, medium, and light lines represent 0.5, 0.75, and 1Hz, respectively.

IDEs. Figure 4.3 shows a schematic of the IGE electrode design. The device design 34 allows the fabrication process of one layer to be repeated to create a multilayered structure. The feature sizes (i.e. electrode width and spacing) are relative to the ﬁlm thickness, hence on the scale of several microns. Contrary to IDEs where positive and negative electrodes are patterned on

59 Top copolymer

Copolymer with negative IGE

Copolymer with positive IGE

Copolymer with negative IGE

Copolymer with positive IGE

Silicon wafer

Figure 4.3. Illustration of IGE layers. The device would be strained in the direction of the curved electrodes. Each layer contains an electrode of a different polarity. The same pattern is used in all layers, opposite polarities are just shifted by half a grid size. the same surface of the film, IGEs have the positive and negative electrodes on opposite surfaces, as in PPEs. This reduces the chance of electrodes shorting due to fabrication defects or usage. IGEs also incorporate a grid structure that provides more support to the electrode branches, unlike the branches in IDEs that are only fixed on one end. This also provides additional paths for current in case there is a break in the branch. IDEs are generally used on piezoceramics that experience maximum strains on the scale of 0.1%, so there is a risk of breaking the electrode rails when utilized in the copolymer under 1-3% strain. Damage to the electrode rail could potentially disable a large portion of the electrode structure, which is a concern especially in wearable applications. Serpentine electrodes have been shown to increase electrode

60 compliance in stretchable batteries [87]. Similarly, the rails in this design are given a serpentine shape as shown in Figure 4.3.

4.3 Simulation and Analysis

Electrostatic simulations of IDE and IGE were performed using FEM software (COMSOL). Figure 4.4(a) shows the electric ﬁeld lines through a representative volume element (RVE) of the IDE (top) and IDE (bottom), where the rainbow colored sections represent the active zones in the analytical model and the white areas represent the dead zones. Since the electrodes will be used to pole the material, it is assumed that the local vector at any point in simulated ﬁeld approximates

the polarization direction (i.e. the direction of d33) at that location. This model includes a 50nm thick capping layer in between the layers, but it was shown to have almost no eﬀect on the electric ﬁeld even when the dielectric constant is low.

The RVE consists of the section between electrodes (length se) and half of the

space under the electrodes (length we/2) on each end for one layer of ﬁlm (height

tp and width bp), as shown in Figure 4.4(a). The input force would be acting on

the bp × tp surfaces. The ratio of electrode spacing to electrode width (se/we) is 4 in the RVE depicted. This ratio should be high enough to reduce the size of dead zones, but it also needs be a compromise between the increasing cost and

diﬃculty to fabricate electrodes with smaller we and the increasing output voltage

dictated by a larger se (equation (4.5)). In the current conﬁguration, the open

circuit voltage is already 219V at 2N (2% strain) with we = 6µm and se = 24µm. The magnitude of the simulated electric ﬁeld at a point in the material is used to approximate the amount of polarization that location can achieve. In Figure

4.4(b), the x- and y-components of the average electric ﬁeld, EFEA, in the active

zone is shown as a fraction of the modeled electric ﬁeld, ETH = E3 = V/se, for

diﬀerent aspect ratios (se/tp). When EFEA/ETH = 1 in a part of the material, it is assumed to be fully polarized. It can be seen that as the ﬁlm becomes thinner, this ratio goes to 1. The polarization in the dead zones are not negligible. Figure 4.4(c) shows that

the x-component of the field for the IDE and IGE are as high as 29% of ETH . The x-component of the dead zone electric fields actually help to provide better average electric field estimates for the model. If the electric field in the model is calculated

61 푤 /2 푠 푤 /2 (a) 푒 푒 푒 푏푝

푡푝

x (b) (c) 1.0 1.0

0.8 0.8 IDE

IGE Ex

TH TH

0.6 0.6 IGE Ey

/E /E

0.4 0.4 FEA

IDE FEA E IGE Ex E 0.2 IGE Ey 0.2

0.0 0.0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 se/tp se/tp 25

Figure 4.4. (a) Finite element models and representative volume elements of IDE and IGE. Ratio of simulated electric field (EFEA) to modeled electric field (ETH ) in the (b) active zone and (c) dead zones for different aspect ratios (se/tp). The net vertical electric field for the IDE is zero in the simulation.

from the center of the dead zones (i.e. ETH = V/(se + we)) instead of the edges, the x-component of the ratio EFEA/ETH over the entire RVE is greater than 0.9 at aspect ratios of 3 and 6 for the IDE and IGE, respectively. The RVE of the IDE does not have a net vertical electric ﬁeld component due to symmetry, but the y-component IGE is up to 58% as strong as ETH as shown

62 in Figure 4.4(c), meaning that the dead zones in an IGE could be polarized in the y-direction if ﬁelds much higher than the coercive ﬁeld are used. For example,

at an aspect ratio of 2, the value of EFEA/ETH for the active zone x-component and dead zone y-component are about the same, so both the active zone and the dead zone receive the same ﬁeld during poling. Essentially, this means that the

dead zones will operate in d31-mode and producing a voltage opposite to the active

zones (because d31 and d33 have opposite signs in piezoelectric polymers). This can potentially reduce the power output under x-direction strain due to charge

cancellation. However, d31 is about 3 times lower than d33 in copolymer, as shown

in Table 4.1, which lowers this power loss. Additionally, decreasing we and making the electrode height thicker can reduce the size of the dead zone and the strain induced in it (by increasing the average dead zone stiffness) to further minimize this power loss. The serpentine rails of the IGE have points that overlap, as shown in Figure 4.3. Those areas experience much stronger electric fields than the spaces between the staggered electrodes because the spacing between electrodes is much lower at those points. This can result in dielectric breakdown when poling. This bounds the upper limit of the aspect ratio to a maximum 2 because at least 50MV/m [88] is the coercive field (i.e. field necessary to pole) and about 125-150MV/m is the dielectric breakdown field [89]. Figure 4.4(b)-(c) shows that the field strength is almost equal at the aspect ratio of 2. The effective piezoelectric coefficient for an IGE with these constraints can be estimated as,

se d33 + d31 ∗ se we we d = d33 + d31 = (4.12) 33 s + w s + w se + 1 e e e e we

where se/we indicates the volume ratio of the active zones to dead zones. Equation (4.12) accounts for charge cancellation due to opposite polarities in the active and ∗ dead zones. As se/we is lowered from 10 to 2, d33 drops from -26.3 to -16.3. The ∗ value of d33 is still higher than d31 of copolymer when se/we ≥ 1.16 and higher

than d31 of PVDF when se/we ≥ 4.87. Hence, IGEs on copolymer with se/tp = 2

and se/we ≥ 4.87 will outperform PVDF with PPEs and still be more compliant.

63 Figure 4.5. The electric ﬁeld from an IGE device (shown by the black rectangle at the center) inside PDMS matrix (r = 2.8). The colors represent electric ﬁeld magnitude (V/m).

4.3.1 Electric Field Exposure to Human Body

Both IDE and IGE devices generate electric fields that extend outside of the device itself and into the human body. Using equation (4.10), at 2% strain amplitude, the device produces a voltage amplitude of 154.6V under sinusoidal input. Strain levels of around 1% can be expected during normal operation, so the peak voltage would be around 80V. The IEEE safety standard for human exposure to electromagnetic fields [90] limits the maximum permissible value of an environmental electric field (i.e. field generated outside of the body) to 5kV/m. Figure 4.5 shows the electric field

generated when an IGE device (black rectangle at the center) with se = 24µm has

64 200V applied to the terminals. In this case, the zone with 5kV/m ﬁeld strength (shown in red) extends about 0.8mm away from the device when in PDMS. FEM simulation shows that this distance stays about the same for any material with

a relative permittivity (r) less than 10. Hence, a 1mm thick substrate between the body and the harvester can prevent the 5kV/m electric ﬁeld from reaching the body.

65 Chapter 5 | Multilayered Fabrication Proce- dure for Micron-Scale Electrodes on P(VDF-TrFE)

5.1 Introduction

Polymer-based ﬂexible electronics greatly improve the ergonomics of wearable devices. Piezoelectric materials such as copolymer are especially useful in this area. Fabrication of polymers with patterned micron-sized electrodes over large areas, while maintaining desired electrical properties poses many challenges. Additionally, a polymer with multilayered patterned electrodes can greatly increase design ﬂexibil- ity in wearables. In this chapter, the fabrication process for micron-scale electrodes on a multilayered P(VDF-TrFE) is outlined and capacitance measurements are presented to show preservation of electrical properties.

5.2 Fabrication

The multilayer IGE pattern discussed in Chapter 4 is used to demonstrate this fabrication process. A solution containing 14% P(VDF-TrFE) 70/30 (PolyK Tech- nologies, LLC) by weight and methyl ethyl ketone (MEK) was produced. MEK was used due to a combination of its ability to dissolve the copolymer and its high evaporation rate. The fast evaporation helps with the creation of multiple layers by reducing the amount of time the solution is in a liquid state. Initially, the copolymer

66 Method 3: Capping layer via ALD

• Process • 1. Spin coat photoresist 2. Develop pattern 3. Evaporate gold electrode 4. Lift off resist 5. Atomic layer deposition (ALD) of capping Si wafer P(VDF-TrFE) Photoresist Ti/Au PVA or Al2O3 layer 6. Create second layer of copolymer • Questions 1 4 • What types of materials can be used to make capping layer? • Typical and minimum thickness of capping layer? • Mechanical properties of capping layer? • Flexibility and modulus of copolymer should 2 5 not change greatly • Should be able to handle 1% strain • Dielectric properties capping layer? • ALD process needs to be done at 100°C or lower 3 • Capping layer must be resistant to MEK 6

Figure 5.1. Fabrication process of copolymer with IGE: (1) Create ﬁrst copolymer layer and spin coat a layer of photoresist, (2) pattern resist, (3) evaporate electrode, (4) lift-oﬀ electrode, (5) create capping layer of PVA (spin coating) or alumina (evaporation), and (6) create second layer of copolymer.

solution was spin coated onto an silicon wafer at 1000RPM to produce a layer thickness of 4-5µm. Later, a doctor blade was used to create samples of the same thickness. Then, the copolymer was immediately placed on a hot plate at 100◦C for 5 minutes to normalize internal temperature and promote even evaporation of MEK (boiling point of 79.6◦C). The wafer was transferred to a preheated ventilated oven and annealed for 2 hours at 140◦C to increase crystallinity of the piezoelectric material. Photoresist was patterned using contact lithography onto the copolymer layer, then processed at lower temperatures to avoid melting the copolymer (Figure 5.1, steps 1-2). Titanium (10nm), used as an adhesion layer, and gold (50nm) were evaporated onto the photoresist pattern as electrodes (Figure 5.1, step 3). Lift-off is usually performed with acetone, but it dissolves copolymer. Methanol was able to develop the pattern without affecting the copolymer [91]. This was done by iteratively soaking the sample in methanol for hours and rinsing with water. Some light abrasion was applied to aid in lift-off (Figure 5.1, step 4).

67 5.2.1 Creating Multiple Layers

When another layer of copolymer and MEK solution is created on an existing layer, the interface between the layers dissolves. The high evaporation rate of MEK helps to reduce the depth of the dissolved interface compared to other solvents such as dimethylformamide (DMF). Yet this is still problematic for electrode features that are only several microns wide. The forces involved in creating the top layer warped or destroyed the electrodes on the bottom layer since they were sitting on a liquid film. In the IDE and IGE patterns, it is crucial to maintain the proper spacing between electrodes, otherwise electric field strengths and polarization will be affected. To address this issue, two approaches were empirically tested: (i) reducing the forces involved in fabricating the top layer, and (ii) using a protective material at the interface (i.e. capping layer). Empirical trials showed that the warping and damage of the electrodes during the fabrication of the top layer were reduced by tape casting (i.e. using a doctor blade) instead of spin coating. At 14% weight of copolymer in MEK, the doctor blade was able to produce films of approximately 4-5µm thickness consistently. An additional advantage of the doctor blade was that it did not waste as much copolymer as spin coating, because spin coating propels most of the solution off of the wafer. Hence, it is well-suited to large scale production. Two types of materials were used for the capping layer: polyvinyl alcohol (PVA) and alumina (Al2O3). PVA is resistant to MEK and soluble in water. The static relative permittivity of PVA is sensitive to humidity, but for humidities between 14% and 66%, it ranges from 4.6 to 8.4 at room temperature [92]. PVA was dissolved in DI water at 5% weight by stirring aggressively with a magnetic stirrer while heating at 90◦C for several hours. It was spun onto a sample at 4000RPM and cured on a hotplate at 95◦C for 30 minutes which produced film thicknesses of approximately 200-250nm. Alumina was applied to another sample using evaporation for a thickness of 50nm. It has a permittivity of 9.1, which is similar to that of copolymer (9.3).

5.2.2 Defect Reduction Using Multilayer Fabrication

The advantages of multilayered approach to MEMS fabrication can be seen by comparing the IDEs to the IGEs, as discussed in Chapter 4. Figure 5.2 shows the type of defects that can occur in the electrode pattern during fabrication. A

68 Figure 5.2. IDE and IGE patterned on a layer of copolymer. Shorts on the IDE caused by surface defects and electrode delamination are shown by black arrows. The IGE has three broken branches due to a surface defect, as shown by the red circle, but that does not stop the flow of current due to the grid design. A defect that does not cause a short in an IDE can generate a high electric field when poling, shown in the red square. broken electrode branch can stop the flow of current in a portion of the branch. This deactivates the segment of copolymer around that branch. If a break occurs in the rails, which is possible under high strains, this can disable a large segment of the harvester because IDEs only have one set of rails. The multilayered design enables the grid pattern in IGEs and makes it less susceptible to this type of defect. There will most likely be a path for the current despite a broken branch, unless a large number of branches break in a very small area. Short circuit is another type of defect that IDEs are prone to because both

69 positive and negative electrodes are constructed on a single layer. In the top images of Figure 5.2, we can see two examples of the positive and negative voltage branches being shorted by conductive material left over from the lift-off process and electrode delamination. IGEs are immune to short circuit defects like these because electrodes of different polarities are patterned on different layers. Certain defects can also change the local electric field strength in an IDE increasing the chance of dielectric breakdown while poling, shown by the red square in Figure 5.2. For instance, an electrode defect or conductive particle between a positive and negative branch of an IDE that does not short still reduces the distance between those branches. When voltage is applied during poling, a high electric field is generated around the defective point and is likely to cause a short. A strong localized electric field can occur in IGEs only if there is significant reduction in film thickness, but film thickness is much easier to control than electrode defects. These considerations become more important as electrode spacings get smaller.

5.3 Physical Characteristics of Fabricated Copolymer Samples

IGE samples that were created with PVA and alumina capping layers are shown in Figure 5.3. These samples consist of a layer of copolymer on an silicon wafer, patterned electrodes on top of the copolymer, and then a capping layer followed by a second layer of copolymer with patterned electrodes. A single layer IDE device (i.e. copolymer with IDE patterned electrodes on a wafer) of the same area and a thickness of 3.75-4µm is shown for reference. The electrodes for all samples have widths of 6µm and spacings of 24µm. At the top of Figure 5.3, the IGE harvester with alumina capping layer is shown. The average thickness of the active copolymer layer (i.e. the second layer that sits on top of the 50nm alumina) is 5.43µm with a standard deviation of 0.34µm. Crack formation can be recognized on the bond pad and harvesting area of the device which resulted in slight warping of the electrodes branches. This may be because a 50nm layer was too thin block the MEK from seeping through and softening the interface of the bottom copolymer layer, creating a stress mismatch which produced cracks in the brittle alumina. However the entire electrode structure was

70 7

6 Alumina

3 Loss 2 Capacitance (nF)

0 1E+2 1E+3 1E+4 1E+5 1E+6 Frequency (Hz) 7

6 PVA

3 Loss 2 Capacitance (nF)

0 1E+2 1E+3 1E+4 1E+5 1E+6 Frequency (Hz) 7

6 IDE

3 Loss 2 Capacitance (nF)

1 m

휇 0

1E+2 1E+3 1E+4 1E+5 1E+6 100 Frequency (Hz)

Figure 5.3. Microscopic view of the electrodes of the PVA-capped (top) and alumina- capped (middle) two-layer copolymer IGE samples and a sample with IDEs set on a single layer of copolymer (bottom). not aﬀected by this. Minimizing the amount of time the alumina is exposed to liquid MEK may help in reducing cracks. A sample created with chromium/gold electrodes produced the most cracks, as shown in the left image of Figure 5.4, probably due to the brittleness of chromium. Titanium/gold (top image of Figure 5.3) and aluminum electrodes (bottom image of Figure 5.4), on the other hand, showed fewer cracks. The alumina capping layer can be evaporated before or after the electrodes

71 Figure 5.4. Microscope image of the chromium/gold electroded sample (top) and the aluminum eletroded sample (bottom). The aluminum electrode was patterned on top of the alumina capping layer, so cracking on the capping layer broke the electrodes apart as well. are patterned because alumina is resistant to lithography processing conditions. However, patterning electrodes on top of alumina have been observed to damage the electrodes when the alumina forms cracks, as shown in the inset of the bottom image in Figure 5.4. Electrodes cannot be patterned on top of PVA because it is soluble in water and swells when exposed to the developer used in photolithography. In the samples that were fabricated, the electrodes were patterned on top of the copolymer and the capping layer was formed on top of the electrodes. The electrode bond pads (used to connect wires, see Figure 4.1) of the bottom layer electrode pattern were exposed via manual etching of each material layer. Copolymer was etched with a small amount of acetone, PVA was etched with water, and alumina

72 7 7

6 Alumina 6 PVA

5 5

4 4

3 3 Loss Loss 2 Capacitance (nF) 2 Capacitance (nF)

1 1

0 0 1E+2 1E+3 1E+4 1E+5 1E+6 1E+2 1E+3 1E+4 1E+5 1E+6 Frequency (Hz) Frequency (Hz) 7 + - 6 IDE IDE 5

3 - Loss Capping IGE 2 Capacitance (nF) layer 1

0 1E+2 1E+3 1E+4 1E+5 1E+6 + Frequency (Hz)

Figure 5.5. Capacitance and loss tangent (tan δ) are shown for each sample. The electrode widths are 6µm and the electrode spacing is 24µm. The schematic shows that the electric field (green) can avoid the capping layer in the IDE configuration but must go through it in the IGE configuration. was etched by masking the bond pad section with Kapton tape before evaporation and then peeling the tape. The transparency of these materials at these thicknesses allow electrode alignment to be performed without issues. The PVA used to cap the IGE harvester shown in the middle of Figure 5.3 provided very good chemical resistance, evidenced by the lack of damage or warping of the bottom layer electrodes. The active (top) copolymer layer had an average thickness of 3.94µm with a standard deviation of 0.26µm. The copolymer layer was cast immediately after drying the PVA, which prevented moisture from entering it. The humidity in the fabrication facility (clean room) is maintained at 40%, so it can be assumed that the PVA in the fabricated samples have a permittivity of 4.9 [92].

73 5.4 Electrical Characteristics of Fabricated Copoly- mer Samples

The capacitance plots in Figure 5.5 show capacitance for all the samples. Capaci- tance calculation using equation (4.4) yields a value of 0.64nF for an IDE device with the dimensions of the samples. Capacitance of a parallel plate capacitor with the same properties and dimesnsions is 29nF using equation (3.13). Since the IGE design is somewhere in between IDEs and PPEs, the capacitance values for these two configurations can be thought of as the upper and lower bounds, and the capacitances shown in Figure 5.5 fall within these limits. The schematic of Figure 5.5 shows that the device layers (i.e. copolymer and capping layer) are physically connected in series in the IGE configuration and parallel in the IDE configuration between the electrodes. The series configuration can be −1 −1−1 thought of at the worst case scenario since total capacitance Ctot = C1 + C2 (i.e. in series, a low capacitance, which can be a result of low permittivity, will bring down the total capacitance). However, the capacitance is within expected bounds, showing that very thin layers of both PVA and alumina capping layers preserve the dielectric properties of copolymer. This also indicates that multilayer electroded copolymer films made with these capping layer materials can be poled to create thin film copolymer energy harvesters.

74 Chapter 6 | Self-Power Analysis of Wearable Devices Using Human Behav- ioral Data

6.1 Introduction

The performance of energy harvesters in body sensor networks and the dependence of harvesting power profiles on human activity dictate whether BSNs can be self-powered. Performance in real-world conditions is difficult to predict because people have different activity levels and move through different environments. System models of body-worn energy harvesting and storage networks that include human behavioral data can not only predict self-powered ability, but also allow the investigation of multimodal energy harvesting. This chapter develops a framework that translates variables from a human behavioral database into power available for harvesting coupled to an energy harvesting and storage system model, as shown in Figure 6.1. Although some power sources may have a higher power density than others, their burstiness reduces their ability to reliably power a wearable device under constant power consumption. The model provides insight and statistics on the dynamics of power availability, guiding the design of wearable self-powered systems.

75 Input “Typical day” profiles from the Consolidated Human Activity Database (CHAD) level Activity Time

Outdoor Outdoor

Sunset

Sunrise Sunset

Sunrise Indoor Indoor

Irradiance Temperature

Time Time

Mechanical harvester Rectifier and buck- power is estimated boost converter for based on activity level sinusoidal inputs of varying amplitude

Thermoelectric Bipolar boost harvester power is converter for low proportional to voltage input with ambient and skin varying polarity temperature difference Buck\boost converter with MPPT for fixed Photovoltaic harvester input with varying power is calculated optimal impedance from the location and irradiance

Wearable Device Supercapacitor Charge at time 푡1 ↓ Charging/Discharging Model ↓ 푉푠푐 Charge at time 푡2

Figure 6.1. System model block diagram. The activity levels and environmental conditions are estimated from the human activity database and NREL solar irradiance data. The power produced by the energy harvesters is calculated, and losses due to power conversion electronics are applied. Power ﬂows to the wearable device for usage or a supercapacitor (with coulombic eﬃciency and current leakage) for storage.

6.2 Estimating Harvested Power from Human Behav- ior

The Consolidated Human Activity Database (CHAD) was originally developed to determine population exposure to pollutants, hence contains the behavioral logs of

76 thousands of individuals throughout the day. CHAD provides over 54,000 days of detailed human activity and environmental data for individuals in the United States that can be used to estimate the power available for harvesting throughout the day. The data can also be filtered to analyze different demographics and use cases. In this dissertation, we examine office professionals, retired people, and elementary school children. Similar activity databases exist [93] and sensor data from smart phones and smart watches (i.e. accelerometer, gyroscope, GPS, RF/signal strength, and ambient light sensors) can be collected by manufacturers to expand this kind of analysis. Table 6.1 shows the variables in CHAD that are used in this research to estimate the power available for harvesting at any time of the day. CHAD contains 142 activities and 113 locations. Each individual logs their behavior over a day as a series of time-stamped entries. Each entry in a daily log will herein be referred to as an event. The relevant information for each event is the activity performed, start time, end time, and location. Additionally, each daily log also includes average outdoor temperature and maximum outdoor temperature data. The CHAD daily logs were first filtered based on data quality using the database’s own built-in quality variables (i.e. time gap between activities, travel time inconsistencies, and mismatches between activities and locations), and then filtered again to remove the daily logs that were not 24 hours long or missing any of the information shown in the third column of Table 6.1. Geographic solar irradiation data from the National Renewable Energy Laboratory (NREL) [94] and geographic sunrise and sunset times [95] are used to estimate solar power.

6.2.1 Mechanical Power

Human motion is the input to mechanical energy harvesters. The harvester is assumed to be mounted on the individual’s wrist. The activity level, α, varies from 0 (no activity) to 1 (maximum activity) and describes the amount of mechanical power associated with a CHAD activity. Each daily log event is associated with one activity, so each event has one activity level value associated with it. For the mechanical energy harvester, a mapping between the power generated and activity level was created for each activity using estimated average frequency and amplitude of wrist motion. For example, “eating” was estimated to have α = 0.25, which

77 Table 6.1. Relevant CHAD/NREL variables and harvested power for the diﬀerent energy harvesters.

Power Source Harvester Inputs Variables

Displacement, frequency, Mechanical Activity acceleration Time, maximum temperature, Ambient temperature, Thermal average temperature, body temperature location, activity Time, month, location, Solar Irradiance state/zip code, irradiance

has more wrist motion than “watching TV” (α = 0.15) and less wrist motion than “writing” (α = 0.45). Vaguer CHAD activities, such as “indoor chores”, uses a normal distribution based on the estimated peak and average activity levels. Table 6.2 shows the top 10 CHAD activity variables for each demographic (based on the summation of time that activity appeared in that data set) and the associated mean

activity level, α¯, and the standard deviation, σα. The activity level for “travel” depends on the CHAD location, which contains information about the mode of travel. Most mechanical energy harvesters convert human kinetic energy to electricity using electromagnetic, piezoelectric, or electrostatic (i.e. triboelectric) transducers [65]. Kinetic power is difficult to estimate because it is not only a function of the input motion, but also the harvester design. Different harvesters will absorb kinetic power from different directional components of input motion. For example, the output of a pendulum energy harvester depends on in-plane linear acceleration components and the out-of-plane rotational acceleration component [96]. In this analysis, the mechanical energy harvester is assumed to be a wrist-worn inertial device with a proof mass. Inertial harvesters have highly nonlinear models [96] that would be extremely difficult to use with the CHAD database because it does not include any data on wrist motion. Instead, a numerical mapping of output power as a function

78 Table 6.2. Top 10 activity variables in the CHAD database.

Group Activities (α¯, σα)

Professional 1. Sleep or nap (0.03, 0); 2. Work and other income producing activities, general (0.5, 0.1); 3. Work, General (0.5, 0.1); 4. Work, income-related only (0.5, 0.1); 5. Eat (0.25, 0); 6. Participate in passive leisure (0.25, 0); 7. Watch TV (0.15, 0); 8. Read, general (0.15, 0); 9. Travel to / from work (transportation dependent); 10. Travel, general (transportation dependent)

Retired 1. Sleep or nap (0.03, 0); 2. Eat (0.25, 0); 3. Leisure, general (0.375, 0.075); 4. Watch TV (0.15, 0); 5. General household activities (0.525, 0.108); 6. Passive, sitting (0.15, 0); 7. Travel, general (transportation dependent); 8. Read, general (0.15, 0); 9. Shop / run errands (0.45, 0.05); 10. Converse (0.15, 0)

Children 1. Sleep or nap (0.03, 0); 2. Attend K-12 (0.475, 0.108); 3. Watch TV (0.15, 0); 4. Attend full-time school (0.475, 0.108); 5. Eat (0.25, 0); 6. Play games (0.525, 0.108); 7. Participate in sports (0.55, 0.083); 8. Dress, groom (0.45, 0); 9. Attend day-care (0.5, 0.067); 10. Travel for education (transportation dependent)

of the activity level is developed based on a Kinetron, a commercial wrist-worn inertial electromagnetic harvester. Based on the measured power produced by this device [97], the equation, 2 c1+c2α+c3α PKIN = 10 (6.1) offered a good fit, where c1, c2, and c3 are constants. We assume that this mechanical energy harvester is connected to a rectifier and a buck-boost converter to scale up the voltage. Additionally, the Kinetron uses a spring that collects and releases mechanical energy to the generator intermittently, so the sinusoidal decay of each energy burst is similar. As a result, the electronics efficiency is assumed to range between 60% and 70% [98].

79 Table 6.3. Top 10 location variables in the CHAD database.

Group Locations (pout, psun)

Professional 1. Your residence (0, 0); 2. Bedroom (0, 0); 3. Residence, indoor (0, 0); 4. At work : no specific location, moving among locations (0, 0); 5. Office building / bank / post office (0, 0); 6. Laboratory (0, 0); 7. Travel by car (0, 0); 8. Your residence, indoor (0, 0); 9. Living room / family room (0, 0); 10. At hotel / motel (0, 0)

Retired 1. Your residence, indoor (0, 0); 2. Your Residence (0, 0); 3. Bedroom (0, 0); 4. Living room / family room (0, 0); 5. Travel by car (0, 0); 6. Your residence, outdoor (1, 1); 7. Kitchen (0, 0); 8. Other, indoor (0, 0); 9. Other’s residence, indoor (0, 0); 10. Hospital / health care facility / doctor’s oﬃce (0, 0)

Children 1. Bedroom (0, 0); 2. At school (0, 0); 3. Living room / family room (0, 0); 4. Your residence, indoor (0, 0); 5. Kitchen (0, 0); 6. Travel, general (0.097, 0.097); 7. Your residence, other outdoor (1, 1); 8. Other’s bedroom (0, 0); 9. Bathroom (0, 0); 10. Other’s living room / family room (0, 0)

6.2.2 Thermal Power

Thermal power comes from heat flux produced by a temperature difference which can be converted into electricity via the Seebeck effect. For each CHAD location, the probability of an individual being exposed to indoor air or outdoor air was designated by the number pout between 0 and 1. This value is exactly 0 or 1 for most locations such as “kitchen” (0) and “parking lot” (1). However, some locations can contain either indoor or outdoor temperature. For example, a value of 0.5 was assigned to the “garage” location, so half of these events occur indoors and half occur outdoors. The location information is also used to update the activity level for the travel activity using data from the National Household Travel Survey [99]. Table 6.3 shows the top locations for each demographic ranked by the amount of time spent in each location. The amount of thermal power harvested is a function of the temperature difference between the skin and the environment. The temperature of the environment is

80 estimated based on whether the person is in a temperature-controlled space (indoors) or exposed to environmental temperature (outdoors). The outdoor temperature is calculated using the average and maximum temperature recorded in CHAD and is assumed to be sinusoidal over a 24-hour period. The time delay between maximum temperature and solar noon is assumed to be 3 hours here, but this parameter is location dependent [100]. Hence, the outdoor ambient temperature at any time during the day can be described by,

2π t + t T (t) = (T − T ) sin t − rise set + τ + T (6.2) amb mx av 24 2 t av where Tmx is the maximum temperature, Tav is the average temperature, trise is the sunrise time in hours, tset is the sunset time in hours, and τt is the time delay. If the location is indoors, the temperature ranges uniformly between 68◦F and 72◦F. We assume that the TEG is worn somewhere on the forearm or wrist. This allows us to neglect clothing and perspiration eﬀects in moderate temperatures. The analytical model of the TEG [101] is simple enough to directly incorporate into the system model. The total thermal resistance is,

1 1 Rtot = RT + Rair + Rskin = RT + + (6.3) hAT kAT where the thermal resistances of the TEG, air, and skin are represented by RT , Rair, and Rskin, respectively. Rair and Rskin are estimated by the convection coefficient, h, the conduction coefficient between the skin and the TEG, k, and the area of the 2 TEG, AT (assumed to be 5cm ). The convection coefficient is influenced by activity level since the TEG is assumed to be worn near the wrist and the conduction coefficient depends on how well the TEG adheres to the human body. The open circuit voltage of the TEG is given by,

VOC = β∆Teff (6.4)

81 where β is the Seebeck coeﬃcient and,

RT ∆Teff = ∆T Rtot  (6.5) (Tskin − Tamb) , (Tskin − Tamb) ≤ ∆Tlim ∆T = ∆Tlim, (Tskin − Tamb) > ∆Tlim

∆Tlim is the maximum temperature diﬀerence allowed due to clothing and comfort

of the individual, and Tskin and Tamb are the skin and ambient temperatures, respectively. The maximum power occurs when the load resistance is matched to

the electrical resistance of the TEG legs (Rlegs), which results in half of the voltage ﬂowing through the load.

1 2 2 2 VOC VOC PTEG = = (6.6) Rlegs 4Rlegs

The thermoelectric harvester requires a bipolar boost converter because the ambient temperature can be greater or less than the temperature of the skin. This allows voltage to be greater than zero at all times. The eﬃciency of an oﬀ-the-shelf (COTS) boost converter [98] is used in this work.

6.2.3 Solar Power

The amount of sunlight that an individual is exposed to is a function of the CHAD

location for an event. Similar to pout used to estimate ambient temperature, the

probability of being exposed to sunlight at a certain location is described by psun between 0 and 1, as shown in Table 6.3. For example, “kitchen” has a value of 0, “parking lot” has a value of 1, and “garage” has a value of 0.3. Each CHAD day also has information on which state in the United States the activities took place and during what month. The NREL database provides average global horizontal irradiance (GHI) over a single day for diﬀerent U.S. states during diﬀerent months, along with the minimum, maximum, and standard deviation of those values. Using the state and month information for a CHAD day, the solar irradiance is estimated using a normal random variable with the mean and standard deviation extracted from the NREL database, and bounded between the NREL minimum and maximum. If we assume that the radiation intensity is sinusoidal

82 throughout the day, the peak irradiance can be determined by,

24π Φmx = Φav (6.7) 2 (tset − trise) where Φav is the average irradiance for that day. The outdoor irradiance is then given by the equation below. t − trise Φout(t) = Φmx sin π (6.8) tset − trise

Indoor irradiance is approximated by,

Φin(t) = Φaf + fwinΦout(t) (6.9)

where Φaf is the irradiance from artiﬁcial light, assumed to be constant in this simulation, and fwin reduces the outdoor light intensity to approximate sunlight entering through windows. These parameters are estimated based on data in [102]. The total irradiance received by the energy harvester, based on whether the individual is indoors or outdoors, during the day or night, and is awake or asleep, is given by,  fwrxshdΦout(t), out AND day AND awake   fwrxshdΦin(t), in AND day AND awake Φ(t) = (6.10) fwrxshdΦaf , in AND night AND awake   fwrxshdΦout(t), (out AND night) OR asleep where fwr accounts for a reduction in eﬃciency due to the device being wearable (i.e.

flexibility and orientation effects), and xshd is a normal random number estimating the average amount of shade during an event. As with the other harvesters, it is assumed that the photovoltaic harvester is also worn on the wrist or forearm. Since the wrist is usually not normally oriented to the light source, the parameter fwr is taken to be a conservative value of 0.25. The average shade, xshd, is a normal random variable with a mean of 0.4 and a standard deviation of 0.12. Power from an artificial light source is generally inversely proportional to the distance from the source [66], but it is assumed to be constant for indoor lighting

83 in this simulation. The power produced by a PV cell depends on its eﬃciency,

PSOL = ηΦAS (6.11)

where η is the solar cell efficiency, and AS is the area. In this work, we assume the solar cell has an area of 5cm2 and an efficiency of 10% [103]. At a fixed voltage, the current increases with irradiance [104]. Hence, solar cells are current sources in a circuit and have a maximum power point voltage. In a wearable application, lighting conditions change very rapidly, and MPPT would be ineffective. As a simplification to avoid maximum power point tracking (MPPT), the maximum power point voltage can be assumed as approximately 75% of the open-circuit voltage [105]. Here, the electronics efficiency is assumed to range uniformly between 25% and 35% due to a lack of MPPT [106].

6.2.4 Demographic Data

Three demographics in the CHAD database were examined: office professionals, retired people, and elementary school children. Office professionals were extracted from the database by finding individuals who were employed full-time and had executive, administrative, managerial, professional, or administrative support listed under their occupation variable. Retired individuals were not employed and over the age of 66 (retirement age in the United States). Individuals aged 6 to 11 (age of elementary school students in the United States) made up the children demographic. Additionally, weekend days (i.e. Saturday and Sunday in USA) and days with erroneous or incomplete data were filtered out. This resulted in 1,078 days for the ‘professional’ demographic, 2,435 days for the ‘retired’ demographic, and 1,296 days for the ‘children’ demographic. Figure 6.2 shows the average power harvested by each group using the different energy harvesters using equation (6.1), (6.6), and (6.11) scaled by their respective electronics efficiencies. The power levels shown here are estimates for specific harvester designs and are not meant to be used to directly compare energy harvesting technologies. They can, however, be used to compare power generation between different demographics. Professionals produce the highest mechanical power, which is probably due to performing occupational activities with long periods of wrist motion. Retired people harvest the most solar power, which is most likely due

84 KIN SOL TEG

8 80 10

W] W] W] 6 60

4 40 5

2 20

Average Power [ Power Average [ Power Average [ Power Average 0 0 0

Children Retired Children Retired Children Retired Professional Professional Professional KIN SOL TEG

80 15

W] W] W] 400 60 300 10 40 200 5

20 100

Maximum Power [ Power Maximum [ Power Maximum Maximum Power [ Power Maximum 0 0 0

Children Retired Children Retired Children Retired Professional Professional Professional

Figure 6.2. The average power harvested by the three types of energy harvesters used in this simulation for different demographics based on CHAD data. The error bars show the standard error. The bottom plots show the maximum power produced each day averaged over the whole set for each harvester. KIN is the mechanical harvester, SOL is the solar harvester, and TEG is the thermoelectric harvester. to the fact that children and professionals are often indoors due to education and occupations, respectively. The average thermal energy of all three groups is about the same. The standard error shown in Figure 6.2 can be thought of as a measure of the variety in the behavior of that demographic set. It should be noted that since CHAD compiles data from several scientific studies, the population in the demographic sets are more concentrated to certain areas in the USA than others. The CHAD days are also concentrated to a certain time of the year for each demographic. The top five states where the children in this study are located are California (348), Michigan (55), Ohio (53), New York (52), and North Carolina

85 (47). Retired people are concentrated in Washington (610), California (537), Texas (318), North Carolina (234), and Georgia (165). Professionals who fit the filtering criteria are only found in two states: North Carolina (907) and California (171). The top five months when the children logged their daily activities are May (220), April (212), October (129), January (118), and November (108). Retired people recorded their daily activities most often during the months of August (548), July (375), February (187), September (184), and October (175). Professionals logged their daily activities during July (134), August (131), December (131), April (107), and March (92) the most. These factors add a bias to the environmental conditions of the demographic sets, influencing the lifestyle of the individuals and affecting the average power values of the harvesters. The maximum power generated by the different harvesters can occur at different times during the day. The daily logs were separated into 24 one-hour bins and the power was averaged over each one-hour time span to find the hour of the day where the most power is harvested. The number of times the maximum power occurred in each bin was tallied for each demographic set and is shown in Figure 6.3(a)-(c). For the solar harvester, the peak power predictably occurs at about the same time for all demographics. There are spikes showing a number of peak power events in the afternoon for the children demographic set, probably due to outdoor recreation. On the other hand, retired and professional demographics have their peak power events concentrated earlier in the day. Energy intensive processes such as data broadcasting can be initiated during or soon after the maximum power event. Figure 6.3(d)-(i) shows the time-varying average and standard deviation of power for each demographic set. This information can be used to study worst case scenarios and create randomly generated days. The profile of the results in Figure 6.3(a)-(c) are also similar to those in Figure 6.3(d)-(f), indicating that in most cases, the majority of generated power tends to be concentrated around the time when the hourly average maximum occurs. It can be seen that the peak standard deviation of the mechanical and solar energy harvesters are on similar scales, while their mean values are orders of magnitude apart. The distribution of the operational time of these two harvesters also varies. On the other hand, the TEG has a low standard deviation due to its steady energy generation. This gives us three power profiles with different levels of burstiness. Burstiness describes the randomness in the intermittency and magnitude

86 of real-world processes. For example, human behavior, natural phenomenon, and heartbeats have burstiness values of around 0.5, 0.2, and -0.7, respectively [107]. The burstiness parameter is deﬁned by Goh and Barabási as,

σ − µ B = p p (6.12) σp + µp where µp and σp are the mean and standard deviation of a process time series. Ki- netic energy yields a high amount of burstiness (B ≈ 0.74, 0.77, 0.76 for professional, retired, and children, respectively), solar energy is medium (B ≈ 0.44, 0.48, 0.48), and low burstiness comes from thermal energy (B ≈ −0.52, −0.51, −0.48). This agrees with expected values because kinetic energy is purely based on human behavior, solar energy is based on a combination of behavior and natural phenomenon, and thermal energy depends mostly on the metabolism, somewhat on natural phenomenon, and very little on behavior.

6.3 Energy Storage Model

The energy storage element acts as a buffer for differences between energy harvested and energy consumed. The two main types of energy storage for wearable devices are batteries and supercapacitors. Batteries generally have higher energy densities and low energy leakage compared to supercapacitors. On the other hand, supercapacitors have higher power densities and can be cycled many more times. The features of the supercapacitor make it well-suited as a buffer for a self-powered wearable system, so it is used as the energy storage element.

6.3.1 Model Derivation

Many approaches to modeling supercapacitors exist [108], but an equivalent circuit model is sufficient for this analysis. The simplest equivalent circuit models for supercapacitors typically have a capacitor, an equivalent series resistance (ESR) to model charging efficiency, and a leakage resistor to model the current leakage. The output voltage from the electronics is assumed to be stable, rectified, and boosted to the maximum voltage of the supercapacitor to enable the flow of charge. Figure 6.4 shows an equivalent circuit model of the supercapacitor.

87 a) KIN - Time of max. d) KIN - Average g) KIN - Std. Dev. 15 20 250

200

15 W]

10 W] 7 7 150 10 100

% Samples % Power [ Power Power [ Power 5 50

0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Time [hrs] Time [hrs] Time [hrs] b) SOL - Time of max. e) SOL - Average h) SOL - Std. Dev. 25 250 400

20 200

300

W] W] 7 15 7 150 200

10 100

% Samples % Power [ Power Power [ Power 100 5 50

0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Time [hrs] Time [hrs] Time [hrs] c) TEG - Time of max. f) TEG - Average i) TEG - Std. Dev. 10 11 6

8 5 W]

W] 10 7 6 7 4

4 3

% Samples %

Power [ Power [ Power 2 2

0 8 1 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Time [hrs] Time [hrs] Time [hrs]

Figure 6.3. Average power statistics for kinetic, solar, and thermal harvesters: (a-c) statistical distribution of the time (hour) of maximum power generation, (d-f) average power harvested, and (g-i) power standard deviations. The professional, retired, and children demographic sets are indicated by the dark, medium, and light lines, respectively.

The conservation of energy in the supercapacitor is given by,

Esc = Ein − Es − EL (6.13)

where Ein is the harvested energy being stabilized by the electronics, Es is the energy used by the BSN, and EL is the energy leaked by the supercapacitor. This

88 can be rewritten in terms of power as, Z Z Z Z ncap 2 ncap Vsc(t)Isc(t)dt = Pin(t)dt − Ps(t)dt − Vsc(t) dt (6.14) T T T RL T where T is a time interval, Vsc is the voltage of the supercapacitor, Isc is the current entering the supercapacitor, and ncap is the number of parallel supercapacitors in

Figure 6.4. The parameter ncap allows us to eﬀectively vary the size of the supercapacitor using the parameters of a known supercapacitor cell. Pin is the harvested power remaining after the electronics from the diﬀerent harvesters indicated by

P1,P2, ..., Pnh in Figure 6.4, where nh is the number of harvesters in the network.

Ps is the power consumed by the BSN (assumed constant) and RL is the leakage resistance. If the power harvested and power consumed are constant over a small time interval [t1, t2], we can write an equation for current from equation (6.14) as,

dVsc(t) Pin − Ps Vsc(t) Isc(t) = C = − (6.15) dt ncapVsc(t) RL where C is the capacitance of one capacitor in Figure 6.4 and t ∈ [t1, t2]. This

Bernoulli diﬀerential equation can be solved analytically for Vsc(t) and Isc(t) as shown below. r 2(t−t1) 2 2 2 − R C Vsc(t) = Vp − Vp − Vsc(t1) e L

2(t−t1) 2 2 − R C Vp − Vsc(t1) e L Isc(t) = (6.16) q 2(t−t1) 2 2 2 − R C RL Vp − Vp − Vsc(t1) e L

2 (Pin − Ps) Vp = RL ncap

The amount of charge in the supercapacitor can be determined by,

Q(t) = ncapCVsc(t) (6.17)

and the charge added to the supercapacitor over time interval [t1, t2] can be

89 Supercapacitor with 푛푐푎푝 “cells” Output from electronics

푃푛ℎ 푉푖푛 퐼 푛ℎ 퐶 퐶 퐶

푅퐿 푅퐿 푅퐿

푉푠푐 푉푠푐 푉푠푐

퐼퐿 퐼푠푐 퐼퐿 퐼푠푐 퐼퐿 퐼푠푐 퐼푏 퐼푏 퐼푏 푃2 푉 푖푛 퐼2 Sensors 푛푐푎푝퐼푏 푃푠

푃1 푉 푉푖푛 퐼1 퐼 푎 푖푛 퐼푠

Figure 6.4. Schematic of the supercapacitor model. calculated using the equation below.

Z t2 41 Q(t2) = Q(t1) + ηscncap Isc(t)dt = Q(t1) + ηscncapC [Vsc(t2) − Vsc(t1)] (6.18) t1

The ESR is typically used to model coulombic eﬃciency in equivalent circuit models.

The coulombic efficiency is modeled here with an efficiency factor, ηsc, applied to the current entering the supercapacitor. It is usually a function of the aging of the supercapacitor (i.e. number of cycles) and influenced by different physical properties and defects. In this model, the leakage resistor, RL, is 12.5MΩ, and

ηsc = 0.95 when charging (Isc > 0) and 1 otherwise, based on the electrochemical double layer capacitor (EDLC) in [109].

6.3.2 Computation Process

The initial charge in the supercapacitor is known at the beginning of each time step and the voltage is calculated using equation (6.17). Then, a failure condition

90 is checked using,  Vsc(t1),Vsc(t1) ≥ Vs Vsc(t1) = (6.19) Stop,Vsc(t1) < Vs where Vs is the minimum voltage allowed by the boost converter of the sensor. This is the condition for a vigilant monitoring system, where the sensors must always be powered. Then the voltage and current are evaluated using equation (6.16) based on the input power, Pin and sensor power Ps. The charge of the supercapacitor is calculated using equation (6.18) and is bounded by,  ncapCVsc(t2), 0 < Vsc(t2) < Vsc−max  Q(t2) = ncapCVsc−max,Vsc(t2) ≥ Vsc−max (6.20)   0,Vsc(t2) ≤ 0

The process is iterated until the simulation has ended or a failure condition is reached. Figure 6.5 shows an example of the simulation of a single day with mechanical, thermal, and solar harvesters charging the supercapacitor and providing Ps to the wearable device. This day comes from the ‘Professional’ set and occurs during the month of June in North Carolina. The average temperature of this day was 79.1◦C with a high of 95◦C. On that day, the temperature of the skin was closer to outdoor temperature than indoor temperature. Hence, the downward spikes in the temperature diﬀerence plot (Figure 6.5(b)) indicate the times when the individual went outside.

In the simulation, the power harvested by a single harvester, Pi (where i =

1, 2, ..., nh), is normalized by hPharvii,j, which is the average power of that harvester for demographic j (where j = Professional, Retired, Children), shown in Figure 6.2. We examine normalized values because the power generated by an energy harvester can always be controlled by changing its dimensions (i.e. proof mass for mechanical energy harvesters and surface area for TEG and PV harvesters) or through the evolution of technology, as they move towards their theoretical limits [38]. The power used by the BSN is deﬁned by a power factor, which is Ps/hPharvii,j. Figure 6.5(c) shows the power harvested by each device normalized by their respective average harvested powers in the professional demographic. In Figure 6.5(d), it can

91 1 20 Sol. Act. 15 0.8 Temp. 10 | T| 0.6 | T | 5 eff

0.4 0 0 5 10 15 20 2 0.2 Q out 1.5 Q in 0 Q 0 5 10 15 20 1 SOL Q 15 KIN P Q SOL 0.5 TEG P KIN P 0 TEG 0 5 10 15 20 10 4

5 2

0 0 0 5 10 15 20 0 5 10 15 20 Time [hrs] Time [hrs]

Figure 6.5. Typical simulation results from a CHAD day (24 hours starting at midnight). a) The solar irradiance, activity level, and outdoor temperature are inputs to the system shown in a normalized plot. b) The temperature diﬀerence is based on the location of the individual and the temperature diﬀerence across the TEG is calculated using the TEG model. c) The power produced by each harvester, normalized by the average power produced by that demographic using that harvester. d) The cumulative charge entering and exiting the supercapacitor normalized by capacitance and the contributions from each harvester. e) The supercapacitor voltage over time, where the dashed lines represent the upper and lower bounds. be seen that the cumulative charge contribution by each harvester is about the same at the end of the day due to this normalization.

92 6.4 Monte Carlo Simulation

Each energy harvester is simulated using the Monte Carlo method for all random variables (including Ps) and each demographic 2000 times. The starting time of each simulation is randomized by selecting a random event from the daily log and starting the simulation from that point. The initial energy of the supercapacitor is taken as 50% of the maximum.

6.4.1 Performance and Discussion

Figure 6.6 shows the success rate of each harvester as a function of power factor, where a success is defined as being able to maintain the supercapacitor voltage at or above 0.5V. The combined results for all demographics are shown. The lengths of the simulations are 7, 21, and 63 days, as indicated by the solid, dashed, and dotted lines, respectively. The minimal difference between those three simulations shows that the initial conditions did not factor into the results of the 21 and 63 day long simulations. In order to ensure that the success rate shown in Figure 6.6 is not affected by the size of the supercapacitor, the capacitance was increased 10 times yet still produced the same results. Hence, Figure 6.6 shows only the effect of intermittency on wearable energy harvesters, and is not affected by initial conditions or low energy storage capacity. Figure 6.6 can also be used to size the harvesters based on the required success rate for an application. For example, if 95% success is required, then the solar and kinetic harvesters must be sized such that the average power harvested is 5 times higher than the power consumption of the wearable device. On the other hand, if the wearable device can operate intermittently (i.e. power sensors until supercapacitor charge is low, shutdown and charge, and then power sensors again when supercapacitor is charged), then a high success rate is not required. The system was also simulated using variable power consumption profiles governed by a uniform distribution. These profiles were constructed from square waves with a 60 minute period, 50% duty cycle, uniformly distributed random amplitudes, and an average power of Ps over 24 hours. Power consumption profiles with average burstiness values of 0.12, 0.30, and 0.46 were simulated for 63 days. However, the results showed that a uniform random variation in power consumption

93 100

Success [%] Success 40

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 P /

s harv

Figure 6.6. The success rate of solar (dark), kinetic (medium), and thermal (light) energy harvesters versus power factor. Success is defined as being able to maintain a supercapacitor voltage above 0.5V for 7 (dotted), 21 (dashed), and 63 (solid) days. does not affect the overall performance shown in Figure 6.6. Under these power consumption profiles, burstiness of the harvested power had a negative effect on success rate, as evidenced by the success rate of the steadiest harvester, the TEG. The constant power production of the TEG allows it to keep the BSN running overnight, which is where all three the harvesters failed most often. Intermittency also causes the solar and mechanical harvester to be more dependent on the supercapacitor, which increases the losses from leakage current and coulombic efficiency. Each harvester has a different feature that is useful to a self-powered system. The photovoltaic harvester has the highest achievable power density and can provide a high power over a narrow, but predictable window, which can be used for data

94 broadcasting. TEG provides a steady power, useful for vigilant sensing throughout the day. The mechanical harvester correlates best with many physiological signals, which may in turn correlate with a realistic power consumption proﬁle for a more energy balanced operation. For instance, a higher activity level would generate more power but also cause a faster heart rate. This would require an ECG sensor to use a higher sampling rate to sense accurately, and therefore increase the energy cost.

95 Chapter 7 | Conclusions and Future Work

This dissertation contributes to wearable assistive technologies including the design, modeling, fabrication, and analysis of devices. Two main areas of research were explored: modeling of energy harvesting devices and the utilization of PVDF-based piezoelectric polymers for actuation and sensing.

7.1 Conclusions

Relaxor ferroelectric terpolymer unimorph actuators were investigated and a linearized time-varying model was formulated. The model accommodates viscoelasticity using multiple first order ODEs analogous to cascaded parallel RC circuits, and is well suited for design of haptic feedback devices. Model-based analysis reveals that slowly changing the bias voltage to move the vibrating actuator towards a body can improve haptic signal strength. Additionally, these unimorph actuators have high transverse tip deflection at very slow actuation rates (825µm for a 9.8mm beam over a 120s ramp) and resonance (1.46mm tip deflection amplitude at 429Hz). The slender form factor, compliance, and light weight of these actuators make them ideal for integration into haptic feedback systems. This functionality was demonstrated on a foot prosthesis. A novel rotary motor that used the vibrations from the cantilever actuators as input was designed and constructed. The motor showed that a small 9mm × 10mm actuator provided a maximum power of about 6.9-8.9µW at 9Hz which yielded a maximum power density between 0.27 and 0.34W/g based on the mass of the active segment of the unimorph. If the volume of the rotary motor is filled with EAP actuators, it may approach power levels similar to electric motors.

96 Soft tissue compliance is an important effect to be considered in chest strain energy harvesters. For EM generators, this compliance combines with gear train friction to produce power blackouts during shallow breathing. For piezoelectric PVDF harvesters, soft tissue compliance limits strain in the stiff PVDF film and lowers the generated power. EM and PVDF harvesters were designed and built, and showed peak power levels of 25mW and 1mW during deep breathing, respectively. Simulation at low frequencies (0.3Hz) of the EM harvester with static friction effects and PVDF harvester showed that EM outperforms PVDF except during the slow, shallow breathing that is prevalent most of the time. Under the same amount of force required for the EM generator to break out of static friction, the PVDF harvester can generate 10µW at 1Hz for a 14.6cm × 6.6cm film. Additionally, the EM generator alone is almost 100 times heavier than the PVDF film, which can be very encumbering. Very thin PVDF films that cover more of the body and are integrated into tight fitting garments have excellent potential to power health monitoring devices. Power outputs from PVDF and P(VDF-TrFE) harvesters with IDEs under the same input forcing were compared using a model. A copolymer harvester with IDEs is capable of producing 1.8 times more power than PVDF with PPEs and produces more power than PVDF with IDEs at the optimal load. A wearable thin film energy harvester with a new IGE electrode pattern was designed. IDEs were compared to IGEs using electrostatic finite element simulations to show that the performance of high aspect ratio IDEs and IGEs are similar. However, due to electrode overlap in small areas of the grid design, the aspect ratio must be limited to less than 2 for copolymer to prevent breakdown during poling. Yet, the effective piezoelectric constant for an aspect ratio of 2 and a suboptimal electrode spacing-to-width ratio of 2 was estimated to be 16.3, which is still higher than the d31 piezoelectric constant for copolymer. Fabrication of micron-sized electrode features on large films of active material like P(VDF-TrFE) expands the design space of many wearable devices. A new fabrication process for flexible copolymer based sensors and actuators over a large area with multiple layers is demonstrated. Capacitance measurements from a single layer IDE device and multilayer IGE devices with alumina and PVA as capping layer materials are shown to be similar, demonstrating electrical functionality and performance of the capping layer method. PVA thin films are the better choice of

97 the two materials due to its chemical resistance, ease of fabrication, and mechanical stability. This process enables not only the fabrication of IGEs, but also other types of flexible electronics using multiple layers of a multifunctional (i.e. actuating, sensing, and energy storing) material like copolymer. A human activity database containing the activities of real people was used to predict self-power ability for different demographics. Power availability profiles were generated from this data and used as the inputs to an energy harvesting and a storage system model. A normalized analysis of the power dynamics of different harvesters was presented. This type of real-world analysis using a large set of behavioral data has not been conducted before. Based on the model, kinetic, solar, and thermal energy harvesters produce 9.3, 16.5, and 65% of their maximum power on average. This reflects the intermittency and variability of solar and kinetic energy harvesting. The amount of power produced also depends on the user. The retired demographic in CHAD, for example, produced 43.5% more solar power than the office professional group. The distribution of power generation during the day also depends on the energy harvesting modality and group, with retired people and children producing more power in the morning and afternoon, respectively. Energy storage has the potential to smooth out the variations in self-power over the day, but not entirely. The bursty kinetic and solar energy harvesters, for example, are 90% successful in providing 30-35% of their average power continuously to a wearable device, while the TEG can perform just as well at nearly 87% of its average power. This information also helps in sizing the different energy harvesting technologies for real-world wearable applications.

7.2 Future Work

This section provides recommendations for continued research on the topics discussed in this dissertation. Improved models, accurate parameterization, and new fabrication techniques are needed.

• Incorporate more physics into the EAP actuator model. The EAP actuator model shown in Chapter 1 approximates the material properties based on experiments because they were purchased from an external vendor. Additionally, the observed viscoelasticity was modeled by a cascaded

98 equivalent circuit model which did not provide insight into the physics of the material. A physics-based actuator model that begins on the microscopic level may provide a better understanding of the underlying mechanisms and eliminate the need for parameter estimation. Furthermore, the EAP haptic device should be studied by applying the appropriate boundary conditions on the ends of the beam to simulate skin. Then, the correct actuation frequency for diﬀerent soft tissue compliances can be determined. The vibrating/impacting operational mode and its use in the rotary motor merits further study. The EAP motor model was highly nonlinear due to impact forcing and using one-way clutches, hence diﬃcult to simulate. The torque versus speed curve of the motor should also be characterized for a larger number of EAPs.

• Measurement of human soft tissue compliance. The chest strain energy harvesters were tested and the soft tissue compliance was represented by a linear spring. However, human soft tissue has nonlinear stiffness. A comprehensive study on soft tissue dynamics of the human body could benefit strain energy harvester optimization for power and ergonomics. Soft tissue compression is also an important factor for the EAP actuator. Compliance from different parts of the human body affect the boundary conditions of the device and shift the resonances. Therefore, studying soft tissue compliance will also enable the use of EAP haptic actuators for a wider range of prosthetic applications.

• Stabilize the micron-scale electrode structure via etching. The capping layer in the fabrication process helped to prevent the interface of the copolymer from dissolving and subsequently warping the electrodes. The capping layer can be avoided if the electrodes are properly supported during the casting of a new copolymer layer. A possible solution to support the electrodes is to etch the lithography pattern onto the copolymer ﬁrst. Then the electrodes can be patterned inside the etched groove which might support them against shear forces enough to cast another layer of ﬁlm using a doctor blade. This method may be able to produce multilayer structures made completely of copolymer.

99 • Increasing the dielectric breakdown strength of the overlapped sections of the IGEs. Solutions to the overlap problem could involve the use of insulating materials between the overlapped electrodes. Etching gaps in the copolymer where the overlap occurs and depositing a material with high dielectric breakdown strength can prevent shorts during poling. Another method may be to increase the thickness of the copolymer beneath the overlapped areas by depositing another compatible material to create a step in the sections between the rails. The electrode and copolymer can then be deposited. This would result in the thickness of the material under the rails to be equal to the sum of the copolymer thickness and step height.

• Pole the multilayer copolymer ﬁlms with capping layers. After fabricating multilayer copolymer samples with PVA and alumina capping layers, the capacitance was used to show the retention of bulk electrical properties. However, the devices were not poled. Dielectric and piezoelectric properties of the copolymer with capping layer should be characterized as part of future work.

• Improve harvester power estimations in self-powered system model. All 142 activity levels in the human activity database were estimated based on the output power levels measured from a Kinetron mechanical energy harvester for only 5 activities. Experimental measurements should be taken for each activity to make more accurate power estimations. Additionally, other random variables in the program, such as shade level and convection for different locations at different times of the year, can be empirically measured as well. RF harvesting and WPT are very active research areas that should be incorporated into the model. Finally, the power consumption profile is not constant in real-world applications, so variable power consumption profiles and power management rules can be included in the system as well to simulate real-world performance.

100 Appendix A| Electroactive Polymer Rotary Mo- tor Model

In this section, the model of the EAP actuated rotary motor is shown, which is a switched linear time-varying system. The model can be simulated, but parameters are diﬃcult to estimate. This model expands on the beam model in Chapter 2.

A.1 Parameters

The following parameters are used in the model:

θ = angle of rotation of the rotor nEAP = number of EAP beam actuators J = moment of inertia of the rotor b1 = viscous friction of rotor b2 = Coulomb friction of rotor kR = return spring constant zR = return spring preload

LR = position of return spring on the rotor kF = surface spring constant cF = surface damping constant w0 = static beam deﬂection

LF = position of EAP beam on rotor

The torque applied to the shaft is T (t).

101 푇 푡

퐽, 푏1, 푏2

휃 푡 푘푅

푐퐹 푘퐹

퐿푅 퐿퐹

푐퐹 휌, 푌, 퐼, 퐿, 퐴 , 푐 , 푐 푘퐹 푐 푠 푎 푧 푀(푡)

푤(푥, 푡) 푥

Figure A.1. Free body diagram of rotary motor (top) and EAP actuator (bottom).

A.2 Equilibrium Condition

The displacement of the beam will be evaluated at Lδ, which is deﬁned as the location where the rotor makes contact with the beam. 58

∞ N N X ∼ X X w(Lδ, t) = wn(Lδ, t) = wn(Lδ, t) = δn(t) = 11×N δ (A.1) n=1 n=1 n=1

Under static equilibrium, the deﬂection of the beam tip is w0 and initial compression of the return spring is zR, which gives the equilibrium condition for the deﬂection at the location of interest,

w0 = 11×N δ0 (A.2) −1 kRzRLR δ0 = −K Q LF where the elements of Qn = φn(L)φn(Lδ) of size N × 1.

102 A.3 Switched Linear Time-Varying System

The equations of motion for the EAP unimorph actuator and rotary motor are shown below, and the conditions for the “switches” are deﬁned. Beam dynamics:

nm ¨ ˙ X Mδ(t) + Cδ(t) + K (δ(t) + δ0) + P Mi(t) + PMb(t) i=1 (A.3) ˙ ˙ = −ΓF (t)Q cF LF θ(t) + 11×N δ(t) + kF (LF θ(t) + 11×N δ(t))

Rotor dynamics:

¨ ˙ Jθ(t) + b1θ(t) + kRLR (zR + LRθ(t)) + (2ΓT (t) − 1) b2 + ΓT (t)T (t)

= −nEAP LF ΓF (t) (A.4) ˙ ˙ × cF LF θ(t) + 11×N δ(t) + kF (LF θ(t) + 11×N δ(t))

Switches for contact (ΓF (t)) and one-way clutch (ΓT (t)):  0,LF θ(t) + 11×N δ(t) > 0 ΓF (t) = 1,LF θ(t) + 11×N δ(t) ≤ 0  (A.5) 0, θ˙(t) ≤ 0 ΓT (t) = 1, θ˙(t) > 0

A.4 State Space Representation

The state space representation uses voltage, spring preload, torque, and Coloumb friction on the shaft as model inputs. This example uses nm = 2.

x˙ (t) = A(t)x(t) + B(t)u(t) (A.6) y(t) = Θx(t)

The matrices are deﬁned below.

˙ ˙ ˙ T x(t) = δ1(t), ..., δN (t), δ1(t), ..., δN (t),M1(t),M2(t),Mb(t), θ(t), θ(t) (A.7)

103 T u(t) = [VL(t), zR,T (t), b2] (A.8) ˙ T y(t) = w(Lδ, t), w˙ (Lδ, t), θ(t), θ(t) (A.9)   0N×N IN×N 0N×1 0N×1 0N×1 0N×1 0N×1  ˆ ˆ   −K(t) −C(t) −P −P −P −Qk(t) −Qc(t)   1  01×N 01×N − 0 0 0 0  τ1   1  A(t) =  01×N 01×N 0 − 0 0 0  (A.10)  τ2   1   01×N 01×N 0 0 − 0 0   τb     01×N 01×N 0 0 0 0 1  ˆ ˆ ∆k(t) ∆c(t) 0 0 0 −k(t) −b(t)   0N×1 0N×1 0N×1 0N×1    0N×1 −Qz 0N×1 0N×1     µ1Mavg 0 0 0   τ1Vavg(t)   µ2Mavg  B(t) =  0 0 0  (A.11)  τ2Vavg(t)   µbMavg 0 0 0   τbVavg(t)     0 0 0 0    kRLR ΓT (t) 0 − J − J −∆b(t)   11×N 01×N 0 0 0 0 0    01×N 11×N 0 0 0 0 0  Θ =   (A.12)  0 0 0 0 0 1 0   1×N 1×N  01×N 01×N 0 0 0 0 1

VL(t) = 2V (t) − Vavg(t) (A.13)

Cˆ (t) = C + ΓF (t)cF Q11×N (A.14)

Kˆ (t) = K + ΓF (t)kF Q11×N (A.15)

Qc(t) = ΓF (t)cF LF Q (A.16)

Qk(t) = ΓF (t)kF LF Q (A.17)

kRLR Qz = Q (A.18) nEAP LF b + Γ (t)n L2 c ˆb(t) = 1 F EAP F F (A.19) J

104 k L2 + Γ (t)n L2 k kˆ(t) = R R F EAP F F (A.20) J Γ (t)n L c 1 ∆ (t) = F EAP F F 1×N (A.21) c J Γ (t)n L k 1 ∆ (t) = F EAP F F 1×N (A.22) k J 2Γ (t) − 1 ∆ (t) = T (A.23) b J

A solution with measured motor parameters (J, LR, LF , zR) and tuned parameters

(b1, kR, kF , b2 = 0, cF = 0) with inputs of 150V peak-to-peak voltage at 9Hz from 4 EAPs and T (t) = 0 is shown in Figure A.4. The top of Figure A.4 shows a frequency down-conversion from EAP actuator to rotor by a factor of 2 and the middle shows both rotor and actuator at the same frequency after the return spring constant was increased. Then, increasing the return spring constant further provided higher rotor displacement as show at the bottom of Figure A.4. This system is sensitive to the simulation time step because the “switching” may not be occurring at the right moment (instead occurring at the next closest time step) causing the initial conditions after “switching” to be incorrect. Additionally, the damping force should be controlled by another switch that checks relative velocity of beam tip to rotor tip, instead of just relative displacement.

105

Beam tip deflection (red) and rotor tip deflection (blue) m] 800

600

Deflection [ Deflection 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s] Voltage 150

100

50 Voltage [V] Voltage 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s] Distance between beam tip and rotor tip

m] 400

200

Distance [ Distance 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s]

Beam tip deflection (red) and rotor tip deflection (blue)

m] 800

600

Deflection [ Deflection 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s] Voltage 150

100

50 Voltage [V] Voltage 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s] Distance between beam tip and rotor tip

m] 300 200 100

Distance [ Distance 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s]

Beam tip deflection (red) and rotor tip deflection (blue) m] 800

600

Deflection [ Deflection 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s] Voltage 150

100

50 Voltage [V] Voltage 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s] Distance between beam tip and rotor tip

m] 300 200 100

0 Distance [ Distance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [s]

Figure A.2. Simulation output showing rotor tip (blue) and beam tip (red) deﬂection, input voltage, and distance between rotor and beam for 3 diﬀerent spring constants.

106 Appendix B| Detailed Fabrication Steps for Multilayer P(VDF-TrFE) with Micron-Scale Electrodes

Detailed fabrication steps performed at Penn State Nanofabrication Facility to create multilayer copolymer with PVA capping layers are listed here. The steps can be repeated to create additional layers.

B.1 Fabrication Process Outline

1. Creating PVA solution: Add wPVA grams of PVA to jar. Add wH2O grams of DI water to jar, where,

1 − xp wH2O = wPVA (B.1) xp

where xp is the weight fraction of PVA in water. Use an eye dropper for

accuracy. Use xp = 0.05 for very thin layers of PVA. Mix with mixing spoon until dissolved. Place a magnetic stirrer in jar, and seal the lid of the storage jar with paraﬁlm to prevent evaporation. Stir solution for at least 3 hour at 180 rpm and 90°C. Remove magnetic stirrer from jar and reseal jar with paraﬁlm.

2. Creating copolymer solution: Add wCP grams of P(VDF-TrFE) (copoly-

mer powder) to jar. Recommend starting with wCP = 8g. Add wMEK grams

107 of MEK to jar, where, 1 − x1 wMEK = wCP (B.2) x1

and x1 is the weight fraction of copolymer in MEK. Use an eye dropper for

accuracy. For a solvent containing only MEK and copolymer, use x1 = 0.14.

If adding IPA later, use x1 = 0.3. Mix with mixing spoon until dissolved. Place a magnetic stirrer in jar, and seal the lid of the storage jar with paraﬁlm to prevent MEK evaporation. Replace evaporated MEK. Stir copolymer solution for at least 1 hour at 90 rpm. Remove magnetic stirrer from jar and reseal jar with paraﬁlm.

3. (Optional) Creating co-solvent: Continuing from previous step, add wIPA grams of IPA to jar, where,

x1 − x2 wIPA = wCP (B.3) x1x2

and x2 is the ﬁnal weight fraction of copolymer. Use an eye dropper for

accuracy. Try x2 = 0.14. Mix with mixing spoon until dissolved. Dissovling and mixing takes time, so these steps must be done in a very low humidity environment to avoid water absorption. Place a magnetic stirrer in jar, and seal the lid of the storage jar with paraﬁlm to prevent MEK evaporation. Replace evaporated MEK and IPA with more IPA. Stir copolymer solution for at least 1 hour at 90 rpm. Remove magnetic stirrer from jar and reseal jar with paraﬁlm.

4. Spin coating PVA: Preheat hot plate to 95◦C. Degas PVA in vacuum container, if necessary, to remove bubbles (NOTE: if there is a magnetic stirrer in the jar, remove it ﬁrst because vacuum will draw out bubbles from it). Cover spin coater bowl with aluminum foil. Center Si wafer onto chuck. Select spin program for PVA (4000RPM at 5% wt. produces 200-250nm). Pour solution evenly onto entire wafer slowly, and then begin spin program. Immediately place wafer on hot plate for at least 10 minutes to dry.

5. Spin coating and annealing copolymer: Preheat hot plate to 100◦C and vacuum oven to 140◦C. Cover spin coater bowl with aluminum foil. Center Si wafer onto chuck. Select spin program for copolymer (1200rpm with 10% wt.

108 produces 2.6µm thickness, 12% produces 3.75µm). Pour solution evenly onto entire wafer slowly and generously, and then begin spin program. Immediately place wafer on hot plate for 5 minutes to normalize internal temperature of ﬁlm. Quickly transfer wafer to vacuum oven with temperature at 140◦C and activate vacuum. Anneal for 2 hours. Try to reseal solution jar as soon as possible to minimize MEK evaporation.

6. Photoresist preparation: Center Si wafer in spin coater, and use eyedropper to collect SPR 3012 resist (and for 6” wafer, collect enough resist to ﬁll the entire eye dropper). After beginning spin program, wait for the wafer to start spinning and dispense resist through hole of spin coater lid within 3 seconds (while making sure to move eyedropper so that the center is not left uncoated). Put wafer on cool plate for at least 30 minutes. Set hot plate to 100◦C (checking with thermometer at multiple points). Prepare a pan containing CD-26 and a pan containing DI water and label them. After wafer has sat for 30 minutes, place in CD-26 bath for exactly 30 seconds, then immediately move wafer to DI water bath and rinse with DI water hose for a suﬃcient amount of time. Dry on towel using nitrogen gas in a circular motion starting from center to push away all the water to the edges and make sure backside is dry. Bake on hot plate for 1 minute and move to cool plate.

7. UV Exposure with MA/BA6: Prepare the 7” mask holder (unplug vacuum feed by rotating the sleeve counter clockwise a few turns, then push sleeve in and pull out hose—double check that the hose is secure). Center mask in mask holder and press ‘Change Mask’. Press ‘Enter’ to activate vacuum. Slide mask upside-down in slot under microscope (making sure to hold mask edges with fingers in case vacuum fails) and press ‘Change Mask’ to clamp mask in place. Use the x, y, and θ positioning knobs to center the wafer stage (checking gaps with fingers). Press ‘Select Program’ to select recipe and choose ‘Hard Contact’, then press ‘Edit Parameter’ and change exposure time to 8 seconds and distance to 100µm. Press ‘Edit Parameter’ again to save. Press ‘Load’ and pull out wafer stage drawer. Put the 6” wafer chuck in the wafer stage centered against the theta mark. Center wafer on wafer chuck by using the flats on the pins as guides, press ‘Enter’ to activate vacuum. Slide wafer stage drawer back into tool fully, and press ‘Enter’ again

109 to allow tool to put wafer and mask into contact. Put aluminum foil over the part of the mask that needs to be blocked. Use the arrow keys move the microscope to the bond pads and align use them to align. Only the right knob on the console works, match that to the left knob and use the focus knob above the eyepiece to focus. Press ‘Exposure’ to apply UV light (LOOK AWAY FROM UV LIGHT). Repeat appropriate steps to create all patterns. Pull out wafer stage drawer after exposure. Press ‘Load’ to expose additional wafers and repeat appropriate steps. Press ‘Change Mask‘, pull out mask holder after machine moves and put on shelf, turn oﬀ vacuum by pressing ‘Enter‘ and remove mask.

8. Developing pattern: Put wafer in CD-26 bath for exactly 1 minute, and transfer to DI water bath and rinse with DI water hose for a suﬃcient amount of time. Dry on towel using nitrogen gas in a circular motion starting from center to push away all the water to the edges and make sure back is dry.

9. Electrode deposition with LAB-18: Set wafer stage temperature to 0°C. Vent the load lock (LL) by pressing ‘Start LL Vent’. While LL is venting, go to ‘Sigma’ software, then ‘Edit’, then ‘Process’. Select titanium and set the ‘SetPt’ to 1.0 A/s and ‘Final Thick.’ to 0.100 kA (10nm). Close and press ‘Yes’ to save changes. Reopen window and select gold and set the ‘SetPt’ to 2.0 A/s and ‘Final Thick.’ to 0.500 kA (50nm). Close and press ‘Yes’ to save changes. Additionally, check that the correct element is selected in the pulldown menu near ‘SetPt’. Go to recipes and check that the four materials loaded in the machine match the materials and positions shown in the recipe list, and that gold and chromium are included. Make sure line 23 of the titanium and gold recipes are set to ‘S’, if not double-click and check ‘Skip recipe item’. Press ‘Update VB’ to save. Once LL is vented, place the wafer in the wafer ring upside down, and put the wafer in the wafer holding arm in the LL. Pinch the back of the ring against the arm to make sure it is properly seated. Close the LL and press ‘Start LL Pump’. Load the sample into the PC by pressing ‘Start Sample Load’. Run recipe by pressing ‘Run Recipe’ and select the titanium recipe from the list, and then press ‘Run’. Monitor e-beam through window and adjust with controller (use left stick to go to ‘Set Data’ and then ‘Position’ and right stick to move beam). During ramp down,

110 record time and PC pressure. Repeat ‘Run Recipe’ for gold recipe. After recipes are complete, press ‘Start Sample Unload’. When sample is unloaded (check visually), press ‘Start LL Vent’. Take out sample from LL, close lid, and press ‘Start LL Pump’. Wait for process to complete before leaving.

10. Lift-off: At Wet Chem: Solvent SS Bench, let the sample soak in methanol for 2 hours in a closed container of methanol. Put sample in another container and rinse with DI water. Dry with nitrogen blower in circular motion. Repeat in a fresh batch of methanol until lift-off is complete. If lift-off is still incomplete, dip in methanol, put on towel, and lightly wipe with a microfiber towel.

111 Appendix C| Full List of CHAD Activities and Locations

All activites and locations in CHAD are listed below with average activity level, activity level standard deviation, probability of exposure to outdoor temperature, and probability of exposure sunlight.

Description Avg act. Std. dev Description Avg act. Std. dev Sleep or nap 0.03 0.00 Other passive leisure 0.25 0.00 Travel, general -999.00 0.00 Go to bar / lounge 0.40 0.00 Eat 0.25 0.00 Exercise 0.70 0.07 Walk, bike, or jog (not in transit) 0.55 0.08 Other repairs 0.53 0.11 Participate in passive leisure 0.25 0.00 Perform music / drama / dance 0.70 0.07 Watch TV 0.15 0.00 Obtain car services 0.30 0.00 Indoor chores 0.53 0.11 Create domestic crafts 0.60 0.00 Outdoor chores 0.53 0.11 Attend theater 0.30 0.00 Read, general 0.15 0.00 Create art, music, participate in hobbies 0.60 0.00 Clean house 0.53 0.11 Read books 0.15 0.00 Other leisure 0.45 0.05 Other services 0.38 0.08 Dress, groom 0.45 0.00 Work and other income producing activities, general 0.50 0.10 Work, income-related only 0.50 0.10 Participate in hobbies 0.60 0.00 Personal needs and care, general 0.35 0.07 Travel during work -999.00 0.00 Prepare food 0.50 0.07 Run errands 0.45 0.05 Listen to radio / listen to recorded music / watch T.V. 0.15 0.00 Care of baby 0.38 0.08 Visit 0.35 0.03 Help and care 0.38 0.08 Travel for goods and services -999.00 0.00 General entertainment / social activities 0.50 0.00 Shop / run errands 0.45 0.05 Golf 0.53 0.11 Travel to/from work -999.00 0.00 Obtain personal care service 0.30 0.00 Shower, bathe, personal hygiene 0.23 0.03 Travel for child care -999.00 0.00 Other personal needs 0.35 0.07 Work of/for religious groups 0.50 0.10 Converse 0.15 0.00 Build a fire 0.55 0.08 Passive, sitting 0.15 0.00 Work for volunteer/ helping organizations 0.50 0.10 Use of computers 0.40 0.07 Work for other organizations 0.50 0.10 Prepare and clean-up food 0.50 0.07 Obtain government / financial services 0.30 0.00 Think and relax 0.03 0.00 Bowling / pool / ping pong / pinball 0.90 0.00 Care of child 0.38 0.08 Help / teach 0.38 0.08 General household activities 0.53 0.11 Do homework 0.45 0.00 Leisure, general 0.38 0.08 Watch 0.15 0.00 Write for leisure / pleasure / paperwork 0.45 0.00 Wash clothes 0.55 0.08 Care of clothes 0.75 0.00 Attend full-time school 0.48 0.11 Shop for food 0.45 0.05 Travel for leisure -999.00 0.00 Shop for clothes or household goods 0.45 0.05 Hunting, fishing, hiking 0.50 0.10 Practice religion 0.25 0.00 Medical care-child 0.30 0.00 Travel for event / social activity -999.00 0.00 Attend adult education and special training 0.48 0.11

Figure C.1. List of CHAD activities with activity level and standard deviation, part 1.

112 Description Avg act. Std. dev Description Avg act. Std. dev Attend a party 0.50 0.00 Repair, general 0.53 0.11 Participate in social, political, or religious activities 0.48 0.11 Attend other classes 0.48 0.11 Travel for personal care -999.00 0.00 Watch recreation 0.30 0.00 Care for pets/animals 0.60 0.00 Travel for education -999.00 0.00 Converse / write 0.45 0.00 Breaks 0.15 0.00 Read newspaper 0.15 0.00 Obtain medical service 0.30 0.00 Other sports and active leisure 0.60 0.10 Medical care 0.30 0.00 Home repairs 0.53 0.11 Dry clean 0.55 0.08 Obtain goods and services, general 0.45 0.05 Use library 0.30 0.00 Repair / maintain car 0.53 0.11 Listen to radio 0.15 0.00 Clean-up food 0.50 0.07 General education and professional training 0.48 0.11 Play games 0.53 0.11 Other education 0.48 0.11 Read magazines / not ascertained 0.15 0.00 Play, unspecified 0.55 0.08 Travel for active leisure -999.00 0.00 Work, general, for organizational activities 0.50 0.10 Play indoors 0.60 0.00 Unemployment 0.23 0.03 Clean outdoors 0.53 0.11 Personal hygiene 0.23 0.03 Talk /read 0.15 0.00 Create art 0.60 0.00 Watch movie 0.15 0.00 Watch adult at work 0.15 0.00 Listen to recorded music 0.15 0.00 Work for professional/union organizations 0.50 0.10 Shower, bathe 0.23 0.03 Work for special interest identity organizations 0.50 0.10 Visit museums -999.00 0.00 Work for political party and civic participation 0.50 0.10 Paint home / room 0.45 0.10 Work for fraternal organizations 0.50 0.10 Participate in sports 0.55 0.08 Work for child / youth / family organizations 0.50 0.10 Other household 0.53 0.11 Work, secondary (income-related) 0.50 0.10 Work, General 0.50 0.10 Repair of boat 0.53 0.11 Participate in outdoor leisure 0.55 0.08 Other repairs 0.53 0.11 Child care, general 0.38 0.08 Attend day-care 0.50 0.07 Travel for passive leisure -999.00 0.00 Attend K-12 0.48 0.11 Other entertainment / social events 0.50 0.00 Attend college or trade school 0.48 0.11 Participate in sports and active leisure 0.60 0.10 Yoga 0.40 0.00 Play outdoors 0.60 0.10 Participate in recess and physical education 0.60 0.10 Attend sports events 0.30 0.00 Watch someone provide childcare 0.15 0.00 Care of plants 0.50 0.00 Watch personal care 0.15 0.00 Other child care 0.38 0.08 Watch education 0.15 0.00 Travel for organizational activity -999.00 0.00 Watch organizational activities 0.15 0.00

Figure C.2. List of CHAD activities with activity level and standard deviation, part 2.

Description Out T Sol Description Out T Sol Residence, indoor 0 0 Wait for bus, train, ride (at stop) 1 1 Your residence, indoor 0 0 At work : no specific location, moving among locations 0 0 Your Residence 0 0 Bowling alley 0 0 Travel by car 0 0 Construction site 1 1 Bedroom 0 0 Amusement park 1 1 Living room / family room 0 0 Beauty parlor / barber shop /hair dresser's 0 0 Within 10 yards of street 1 1 Outdoor garage 1 1 Kitchen 0 0 Travel by bicycle / skateboard /roller-skates 1 1 Your residence, Outdoor 1 1 Farm 1 1 Bathroom 0 0 Travel by Motorcycle / moped /motorized scooter 1 1 Grocery store / convenience store 0 0 School grounds 1 1 At Restaurant 0.2 0.2 Other's residence - Pool, spa 0 0 Other's residence, indoor 0 0 Wait for travel, indoors 0 0 Your residence - Other outdoor 1 1 Garage 0.5 0.3 Parking lot 1 1 Industrial plant / factory / warehouse 0 0 At Church 0 0 Pool, river, lake 1 1 Shopping mall / non-grocery store 0 0 Your residence - Pool, spa 0 0 Other's Residence 0 0 Other indoor 0 0 At Hotel /Motel 0 0 Other's Kitchen 0 0 Other outdoor 1 1 Other travel 0.10 0.10 Office building / bank / post office 0 0 Parking garage 1 0.2 Travel by truck(pick-up van) 0 0 Residence, General 0 0 Basement 0 0 Restaurant, picnic 1 1 Residence, Outdoor 1 1 Travel, general 0.10 0.10 Other, indoor general 0 0 Other's Bathroom 0 0 Other's residence, outdoor 1 1 Your outdoor garage 1 0.3 Library / courtroom / museum /theater 0 0 Repair shop 0.5 0.3 Travel by walk 1 0.8 Travel by boat 1 1

Figure C.3. List of CHAD locations with probability of time spent in outdoor air and sunlight, part 1.

113 Description Out T Sol Description Out T Sol Travel by truck 0 0 Travel by other vehicle 0.5 0 Hospital / health care facility /doctor's office 0 0 Other's Dining room 0 0 Public building / library / museum /theater 0 0 Bar / night club / bowling alley 0 0 Dining room 0 0 At Dry cleaners 0 0 Other, indoor 0 0 Public garage 1 0.3 Park 1 1 Travel by Truck (other than pick-up or van) 0 0 Motorized travel 0.5 0.2 Golf course 1 1 At School 0 0 Other's Bedroom 0 0 Public garage / parking lot 1 1 Other's Study / Office 0 0 Auto repair shop /gas station 1 0.5 Other's Basement 0 0 Bar / Night Club 0 0 Other's utility room / laundry room 0 0 Auditorium, sport's arena / concert hall 0 0 Other indoor 0 0 playground 1 1 Other's residence - Other outdoor 1 1 Other outdoor, general 1 1 Indoor garage 0 0 Your indoor garage 0 0 Other's garage 1 0.3 Study / Office 0 0 Other's indoor garage 0 0 Travel by airplane 0 0 Other's outdoor garage 1 1 Your garage 1 0.3 Other, residence 0 0 Park /golf course 1 1 Travel by unmotorized boat 1 1 Indoor gym / sports or health club 0 0 Non-motorized travel 1 1 Travel by motorized boat 1 1 Travel in a stroller or carried by an adult 1 1 Sports stadium and amphitheater 1 0 Waiting 0.3 0.3 Laboratory 0 0 Other repair shop 1 0.2 Other's living room / family room 0 0 Childcare facility 0 0 Utility room / Laundry room 0 0 Childcare facility, house 0 0 Travel by bus 0 0 Childcare facility, commercial 0 0 Service station / gas station 1 1 Laundromat 0 0 Travel by Train / Subway / rapid transit 0 0 School grounds / playgrounds 1 1 Sidewalk / street / neighborhood 1 1

Figure C.4. List of CHAD locations with probability of time spent in outdoor air and sunlight, part 2.

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124 Vita Tahzib Safwat Education

Pennsylvania State University Ph.D., Mechanical Engineering, 2019. M.S., Mechanical Engineering, 2019. Stony Brook University M.S., Mechanical Engineering, 2011. B.E., Mechanical Engineering, 2010.

Work Experience

Graduate Research Assistant, Pennsylvania State University, 8/2014-5/2019 Graduate Teaching Assistant, Pennsylvania State University, 8/2013-12/2014 Design Engineer, Thomas C. Wilson, LLC, 9/2011-8/2013 Graduate Research Assistant, Stony Brook University, 9/2010-5/2011 Intern/Mechanic, Aviation Repair Technical, Inc., 9/2010-5/2011 Intern, B&B Sheet Metal, 6/2010-8/2010

Publications

• T. Safwat, Z. Ounaies, and C. D. Rahn. Self-power analysis of wearable devices using human behavioral data. (In preparation) • L. Dong, M. D. Grissom, T. Safwat, M. G. Prasad, and F. T. Fisher. Resonant frequency tuning of electroactive polymer membranes via an applied bias voltage. Smart Materials and Structures, 27(11), 114005 (2018). • T. Safwat, Z. Ounaies, and C. D. Rahn. Modeling and design of electromagnetic and piezoelectric chest strain energy harvesters including soft tissue eﬀects. SPIE Active and Passive Smart Structures and Integrated Systems, 2018. • T. Safwat, R. Tosto, M. D. Grissom, and C. D. Rahn. A Dynamic Model of Elec- trostrictive Unimorph Actuators for Haptic Devices. ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2016.